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Journal articles on the topic 'Lacunary Arithmetic Statistical Convergence'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Yaying, Taja, and Bipan Hazarika. "Lacunary Arithmetic Statistical Convergence." National Academy Science Letters 43, no. 6 (2020): 547–51. http://dx.doi.org/10.1007/s40009-020-00910-6.

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2

Huban, Mualla, and Mehmet Gurdal. "On invariant arithmetic statistically convergence via weighted density." Ilirias Journal of Mathematics 9, no. 1 (2021): 23–34. http://dx.doi.org/10.54379/ijm-2021-1-2.

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In this paper, our concern is to introduce the concepts of invariant arithmetic convergence, invariant arithmetic statistically convergence and lacunary invariant arithmetic statistically convergence using weighted density via Orlicz function φe. Finally, we give some relations between lacunary invariant arithmetic statistical φe-convergence and invariant arithmetic statistical φe-convergence via weighted density

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3

Huban, Mualla, and Mehmet Gurdal. "On invariant arithmetic statistically convergence via weighted density." Ilirias Journal of Mathematics 9, no. 1 (2021): 23–34. http://dx.doi.org/10.54379/ijm-2021-9-2.

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In this paper, our concern is to introduce the concepts of invariant arithmetic convergence, invariant arithmetic statistically convergence and lacunary invariant arithmetic statistically convergence using weighted density via Orlicz function φe. Finally, we give some relations between lacunary invariant arithmetic statistical φe-convergence and invariant arithmetic statistical φe-convergence via weighted density.

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4

M., M. Karagama, and B. Ladan F. "ON LACUNARY ARITHMETIC STATISTICAL CONTINUITY FOR DOUBLE SEQUENCES." International Journal of Research - Granthaalayah 5, no. 11 (2017): 22–26. https://doi.org/10.5281/zenodo.1065890.

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5

Fridy, John, and Cihan Orhan. "Lacunary statistical convergence." Pacific Journal of Mathematics 160, no. 1 (1993): 43–51. http://dx.doi.org/10.2140/pjm.1993.160.43.

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6

Kişi, Ömer. "Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions." Journal of Mathematics 2021 (March 4, 2021): 1–12. http://dx.doi.org/10.1155/2021/6655630.

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Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary stati

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7

Kişi, Ömer. "On lacunary I-invariant arithmetic convergence." Malaya Journal of Matematik 9, no. 2 (2021): 1–11. http://dx.doi.org/10.26637/mjm0902/001.

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8

Listán-García, María C., Ömer Kişi, and Mehmet Gürdal. "New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences." Mathematics 13, no. 1 (2025): 164. https://doi.org/10.3390/math13010164.

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This paper explores the concepts of J-lacunary statistical limit points, J-lacunary statistical cluster points, and J-lacunary statistical Cauchy multiset sequences. Building upon previous work in the field, we investigate the relationships between J-lacunary statistical convergence and J*-lacunary statistical convergence in multiset sequences. The findings contribute to a deeper understanding of the convergence behaviour of multiset sequences and provide new insights into the application of ideal convergence in this context.

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9

Bhardwaj, Vinod K., and Shweta Dhawan. "Density by Moduli and Lacunary Statistical Convergence." Abstract and Applied Analysis 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/9365037.

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We have introduced and studied a new concept off-lacunary statistical convergence, wherefis an unbounded modulus. It is shown that, under certain conditions on a modulusf, the concepts of lacunary strong convergence with respect to a modulusfandf-lacunary statistical convergence are equivalent on bounded sequences. We further characterize thoseθfor whichSθf=Sf, whereSθfandSfdenote the sets of allf-lacunary statistically convergent sequences andf-statistically convergent sequences, respectively. A general description of inclusion between two arbitrary lacunary methods off-statistical convergenc

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10

Gökhan, A. "Lacunary Statistical Convergence of Sequences of Real-Valued Functions." Journal of Mathematics 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/573756.

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We introduce the concepts of the lacunary statistical convergence of sequences of real-valued functions. We also give the relation between this convergence and strongly lacunary and pointwise statistical convergence. Furthermore we introduce the concept of a lacunary statistical Cauchy sequence for functional sequences and prove that it is equivalent to lacunary statistical convergence of sequences of real-valued functions.

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11

Nuray, Fatih. "Lacunary weak statistical convergence." Mathematica Bohemica 136, no. 3 (2011): 259–68. http://dx.doi.org/10.21136/mb.2011.141648.

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12

Basarir, M., and S. Konca. "Weighted Lacunary Statistical Convergence." Iranian Journal of Science and Technology, Transactions A: Science 41, no. 1 (2017): 185–90. http://dx.doi.org/10.1007/s40995-017-0188-y.

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13

KARAKAYA, V. "On lacunary ?-statistical convergence." Information Sciences 166, no. 1-4 (2004): 271–80. http://dx.doi.org/10.1016/j.ins.2003.12.005.

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14

Asif Hussain Jan, Asif Hussain Jan, and Tanweer Jalal. "Pringsheim and lacunary $\Delta$-statistical convergence for double sequence on $\mathscr{L}-$fuzzy normed space." Proyecciones (Antofagasta) 43, no. 6 (2024): 1347–60. https://doi.org/10.22199/issn.0717-6279-5817.

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We explore the idea of lacunary $\Delta$-statistical convergence for double sequences on $L$-fuzzy normed spaces. Then, we provide a useful characterization of the lacunary $\Delta$-statistical convergence of double sequences with respect to their convergence in the classical sense and show how our method of convergence is weaker than the usual convergence for double sequences on $L$-fuzzy normed spaces. Towards the end, we give the novel relation between lacunary $\Delta$-statistical cauchy sequence and lacunary $\Delta$-statistical bounded double sequence.

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15

Kişi, Ömer. "Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces". Journal of Mathematics 2021 (18 жовтня 2021): 1–17. http://dx.doi.org/10.1155/2021/6897038.

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In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

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16

Alotaibi, Abdullah, and M. Mursaleen. "Korovkin type approximation theorems via lacunary equistatistical convergence." Filomat 30, no. 13 (2016): 3641–47. http://dx.doi.org/10.2298/fil1613641a.

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Aktu?lu and H. Gezer [Central European J. Math. 7 (2009), 558-567] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. In this paper, we apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem by using test functions 1, x/1-x,(x/1-x)2.

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17

Rashid, M. H. M., and Sameer A. Al-Subh. "Statistical Convergence with Rough I3-Lacunary and Wijsman Rough I3-Statistical Convergence in 2-Normed Spaces." International Journal of Analysis and Applications 22 (July 19, 2024): 115. http://dx.doi.org/10.28924/2291-8639-22-2024-115.

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In this paper, we have introduced the concept of the set of rough I3-lacunary limit points for triple sequences in 2-normed spaces. We have established statistical convergence requirements associated with this set. Furthermore, we have introduced the idea of rough I3-lacunary statistical convergence for triple sequences. Additionally, we have demonstrated that this set of rough I3-lacunary limit points is both convex and closed within the context of a 2-normed space. We have also explored the relationships between a sequence’s rough I3-lacunary statistical cluster points and its rough I3-lacun

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18

Kişi, Ömer. "On Wijsman ℐ2-Lacunary Statistical Convergence for Double Set Sequences". Fasciculi Mathematici 57, № 1 (2016): 91–104. http://dx.doi.org/10.1515/fascmath-2016-0018.

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AbstractThe aim of present work is to present some inclusion relations between the concepts of Wijsman ℐ2–lacunary statistical convergence and Wijsman strongly ℐ2–lacunary convergence for double sequences of sets. Also we study the concepts of Wijsman ℐ2–statistical convergence, Wijsman ℐ2– lacunary statistical convergence double sequences of sets and investigate the relationship among them.

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19

Aral, Nazlım Deniz. "Generalized lacunary statistical convergence of order β of difference sequences of fractional order". Boletim da Sociedade Paranaense de Matemática 41 (24 грудня 2022): 1–8. http://dx.doi.org/10.5269/bspm.50848.

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   In this paper, using a modulus function we generalize the concepts of ∆m−lacunary statistical convergence and ∆m−lacunary strongly convergence (m ∈ N) to ∆α−lacunary statistical convergence of order β with the fractional order of α and ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1 and α be a fractional order).  

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20

Huban, Mualla Birgül. "Lacunary ℐ -Invariant Convergence of Sequence of Sets in Intuitionistic Fuzzy Metric Spaces". Journal of Mathematics 2021 (2 листопада 2021): 1–10. http://dx.doi.org/10.1155/2021/7302292.

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The concepts of invariant convergence, invariant statistical convergence, lacunary invariant convergence, and lacunary invariant statistical convergence for set sequences were introduced by Pancaroğlu and Nuray (2013). We know that ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the lacunary ℐ -invariant convergence of sequence of sets in intuitionistic fuzzy metric spaces (briefly, IFMS). In this study, we examine the notions of lacunary ℐ -invariant convergence W ℐ σ θ η , ν (Wijsman sense), lacunary ℐ ∗ -invariant convergence W ℐ

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21

Braha, Naim Latif, Mikail Et та Yavuz Altin. "Almost lacunary statistical and strongly almost lacunary convergence of order (β,γ) of sequences of fuzzy numbers". Annals of the University of Craiova Mathematics and Computer Science Series 51, № 1 (2024): 82–89. http://dx.doi.org/10.52846/ami.v51i1.1746.

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The main purpose of this article is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of order (β,γ) of sequences of fuzzy numbers with respect to an Orlicz function. We give some relations between strongly almost lacunary convergence and almost lacunary statistical convergence of order (β,γ) of sequences of fuzzy numbers, where β and γ are two fixed real numbers such that 0 β≤γ≤1.

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22

Mursaleen, M. "Korovkin type theorem for functions of two variables via lacunary equistatistical convergence." Publications de l'Institut Math?matique (Belgrade) 102, no. 116 (2017): 203–9. http://dx.doi.org/10.2298/pim1716203m.

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Aktu?lu and Gezer [1] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. Recently, Kaya and G?n?l [11] proved some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence by using test functions 1, x/1+x, y/1+y, (x/1+x)2 +(y/1+y)2. We apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem for functions of two variables by using test functions 1, x/1?x, y/1?y, (x/1?x)2+(y/1?y)2.

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23

NURAY, FATIH. "Some Cesáro-Type quasinormal convergences." Creative Mathematics and Informatics 30, no. 1 (2021): 75–80. http://dx.doi.org/10.37193/cmi.2021.01.09.

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In this paper we introduce the concepts of quasinormal strong Cesaro convergence, quasinormal statistical convergence, lacunary strong quasinormal convergence and lacunary quasinormal statistical convergence of sequences of functions and give some inclusion relations.

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24

Ulusu, Uğur, and Erdinç Dündar. "I-lacunary statistical convergence of sequences of sets." Filomat 28, no. 8 (2014): 1567–74. http://dx.doi.org/10.2298/fil1408567u.

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In this paper we study the concepts of Wijsman I-statistical convergence, Wijsman I-lacunary statistical convergence and Wijsman strongly I-lacunary convergence of sequences of sets and investigate the relationship between them.

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25

Sen, Mausumi, and Mikail Et. "Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces." Boletim da Sociedade Paranaense de Matemática 38, no. 1 (2018): 117–29. http://dx.doi.org/10.5269/bspm.v38i1.34814.

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In this article we introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces and give their characterization. We obtain some inclusion relation relating to these concepts. Further some necessary and sufficient conditions for equality of the sets of statistical convergence and lacunary statistical convergence of generalized difference sequences have been established. The notion of strong Cesaro summability in intuitionistic fuzzy normed linear spaces has been introduced and studie

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26

KONCA, Şükran. "Weighted Lacunary I-Statistical Convergence." Journal of the Institute of Science and Technology 7, no. 1 (2017): 267–77. http://dx.doi.org/10.21597/jist.2017127439.

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27

NURAY, FATIH, and UGUR ULUSU. "Lacunary invariant statistical convergence of double sequences of sets." Creative Mathematics and Informatics 28, no. 2 (2019): 143–50. http://dx.doi.org/10.37193/cmi.2019.02.06.

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In this paper, we introduce the concepts of Wijsman invariant convergence, Wijsman invariant statistical convergence, Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence for double sequences of sets. Also, we investigate existence of some relations among these new convergence concepts for double sequences of sets.

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28

Choudhury, Chiranjib, and Shyamal Debnath. "On lacunary statistical convergence of sequences in gradual normed linear spaces." Annals of the University of Craiova, Mathematics and Computer Science Series 49, no. 1 (2022): 110–19. http://dx.doi.org/10.52846/ami.v49i1.1518.

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In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.

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29

Demirci, Işıl Açık, and Mehmet Gürdal. "On lacunary generalized statistical convergent complex uncertain triple sequence." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 1021–29. http://dx.doi.org/10.3233/jifs-202964.

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In this work, we study the lacunary I -statistical convergence concept of complex uncertain triple sequence. Four types of lacunary I -statistically convergent complex uncertain triple sequences are presented, namely lacunary I -statistical convergence in measure, in mean, in distribution and with respect to almost surely, and some basic properties are proved.

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30

Başarır, Metin, and Şukran Konca. "Weighted lacunary statistical convergence in locally solid Riesz spaces." Filomat 28, no. 10 (2014): 2059–67. http://dx.doi.org/10.2298/fil1410059b.

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In this paper we introduce the concepts of weighted lacunary statistical ?-convergence, weighted lacunary statistical ?-bounded by combining both of the definitions of lacunary sequence and N?rlund-type mean, using a new lacunary sequence which has been defined by Basarir and Konca [3]. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces.

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31

Li, Jinlu. "Lacunary statistical convergence and inclusion properties between lacunary methods." International Journal of Mathematics and Mathematical Sciences 23, no. 3 (2000): 175–80. http://dx.doi.org/10.1155/s0161171200001964.

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A lacunary sequence is an increasing integer sequenceθ={kr}such thatkr−kr−1→∞asr→∞. A sequencexis calledsθ-convergent toLprovided that for eachϵ>0,limr(1/(kr−kr−1)){the number of kr−1<k≤kr:|xk−L|≥ϵ}=0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.

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32

Tripathy, Binod, Ömer Kişi, and Mehmet Gürdal. "Certain aspects of rough I-statistical convergence in probabilistic n-normed space." Filomat 37, no. 24 (2023): 8113–30. http://dx.doi.org/10.2298/fil2324113t.

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The main aim of this investigation is to introduce rough I-statistical convergence in probabilistic n-normed spaces (briefly Pr-n-spaces). We establish some results on roughI-statistical convergence and also we introduce the notion of rough I-statistical limit set in Pr-n-spaces and discuss some topological aspects on this set. Moreover, we define rough I-lacunary statistical convergent, rough lacunary I-convergent, rough lacunary I-Cauchy and rough lacunary I?-convergent sequences in Pr-n-spaces. We obtain several significant results related to these notions.

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33

Çakan, Celal, Bilal Altay, and Hüsamettin Çoşkun. "Double lacunary density and lacunary statistical convergence of double sequences." Studia Scientiarum Mathematicarum Hungarica 47, no. 1 (2010): 35–45. http://dx.doi.org/10.1556/sscmath.2009.1110.

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In this paper, we have defined double lacunary density and investigated the relation between statistical and lacunary statistical convergence of double sequences. Also, we have solved an inequality related to the lacunary statistical limit superior of real bounded double sequences.

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34

Sengul, Hacer, Mikail Et та Huseyin Cakalli. "On (f, I) - Lacunary statistical convergence of Order α of sequences of sets". Boletim da Sociedade Paranaense de Matemática 38, № 7 (2019): 85–97. http://dx.doi.org/10.5269/bspm.v38i7.46259.

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In this paper we introduce the concepts of Wijsman $% \left( f,I\right) -$lacunary statistical{\Large \ }convergence of order $% \alpha $ and Wijsman strongly $\left( f,I\right) -$lacunary statistical% {\Large \ }convergence of order $\alpha ,$ and investigated between their relationship.

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35

Konca, Şükran. "Weighted lacunary statistical convergence of double sequences in locally solid Riesz spaces." Filomat 30, no. 3 (2016): 621–29. http://dx.doi.org/10.2298/fil1603621k.

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Recently, the notion of weighted lacunary statistical convergence is studied in a locally solid Riesz space for single sequences by Ba?ar?r and Konca [7]. In this work, we define and study weighted lacunary statistical ?-convergence, weighted lacunary statistical ?-boundedness of double sequences in locally solid Riesz spaces. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces and give some inclusion relations.

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36

Ömer, Kişi, and Tuzcuoğlu Ibrahim. "Fibonacci Lacunary Statistical Convergence In Intuitionistic Fuzzy Normed Linear Spaces." Journal of Progressive Research in Mathematics 16, no. 3 (2020): 3001–7. https://doi.org/10.5281/zenodo.3973308.

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We investigate the concept of Fibonacci lacunary statistical convergence in intuitionistic fuzzy normed linear spaces. We also introduce here a new concept, that is, Fibonacci lacunary statistical completeness and show that every intuitionistic fuzzy normed linear space is Fibonacci lacunary statistically complete.

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37

Verma, A. K., та Lav Kumar Singh. "(∆mv , f)-lacunary statistical convergence of order α". Proyecciones (Antofagasta) 41, № 4 (2022): 791–804. http://dx.doi.org/10.22199/issn.0717-6279-4757.

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In this paper, we define the space Sαθ (∆mv, f) of all (∆mv, f)-lacunary statistical convergent sequences of order α with the help of unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ mv and real number α ∈ (0, 1]. We also introduce the space ωαθ (∆mv, f) of all strong (∆mv, f)-lacunary summable sequences of order α. Properties related to these spaces are studied. Inclusion relations between spaces Sαθ (∆mv, f) and ωα θ (∆mv, f) are established under certain conditions.

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38

Turan, Ceylan, and Oktay Duman. "Fundamental properties of statistical convergence and lacunary statistical convergence on time scales." Filomat 31, no. 14 (2017): 4455–67. http://dx.doi.org/10.2298/fil1714455t.

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In this paper, we first obtain a Tauberian condition for statistical convergence on time scales. We also find necessary and sufficient conditions for the equivalence of statistical convergence and lacunary statistical convergence on time scales. Some significant applications are also presented.

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39

Karagama, M. M., and F. B. Ladan. "ON LACUNARY ARITHMETIC STATISTICAL CONTINUITY FOR DOUBLE SEQUENCES." International Journal of Research -GRANTHAALAYAH 5, no. 11 (2017): 22–26. http://dx.doi.org/10.29121/granthaalayah.v5.i11.2017.2321.

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40

Savaş, Ekrem, and Richard F. Patterson. "Lacunary statistical convergence of multiple sequences." Applied Mathematics Letters 19, no. 6 (2006): 527–34. http://dx.doi.org/10.1016/j.aml.2005.06.018.

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41

Abdul, Hamid Ganie. "Lacunary sequences related to statistical convergence." Annals of Communications in Mathematics 3, no. 1 (2020): 46–53. https://doi.org/10.5281/zenodo.10043174.

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In this manuscript, our concern is to introduce the new approach of studying the lacunary almost statistical convergence and strongly almost convergence of the generalized difference sequences of fuzzy numbers. Some interesting and basic properties concerning them will be studied. 

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42

Şengül, Hacer, та Mikail Et. "On I-lacunary statistical convergence of order α of sequences of sets". Filomat 31, № 8 (2017): 2403–12. http://dx.doi.org/10.2298/fil1708403s.

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The idea of I-convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P. ; Sal?t, T. and Wilczy?ski, W. I-convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray and Ruckle [Nuray, F. and Ruckle,W. H. Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245(2) (2000), 513-527]. In this paper we introduce the concepts of Wijsman I-lacunary statistical convergence of order ? and Wijsman strongly I-lacunary statistical convergence of order ?, and investigated between their relationship.

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43

SAVAŞ, EKREM. "ON ASYMPTOTICALLY LACUNARY σ-STATISTICAL EQUIVALENT SEQUENCES OF FUZZY NUMBERS". New Mathematics and Natural Computation 05, № 03 (2009): 589–98. http://dx.doi.org/10.1142/s1793005709001507.

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This paper presents the asymptotically lacunary σ-statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and lacunary statistical convergence of fuzzy numbers. In addition, we shall also present asymptotically lacunary σ-statistical equivalent analogs of Savas and Nuray's theorems in Ref. 8.

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44

Jeyaraman. M, Iswariya. S, and Pandiselvi. R. "Generalized Double Statistical Convergence Sequences on Ideals in Neutrosophic Normed Spaces." Neutrosophic Systems with Applications 8 (August 1, 2023): 50–60. http://dx.doi.org/10.61356/j.nswa.2023.40.

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In this present research, having view in the Neutrosophic norm (u, v, w), which we presented I2-lacunary statistical convergence and I2-lacunary convergence strongly, looked into interactions between them, and made a few findings regarding the respective categories. At least went further to look at how both of such case approaches relate to I2-statistical convergence within the relevant Neutrosophic normed space.

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45

Et, Mikail, та Hacer Şengül. "Some Cesaro-type summability spaces of order α and lacunary statistical convergence of order α". Filomat 28, № 8 (2014): 1593–602. http://dx.doi.org/10.2298/fil1408593e.

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In the paper [32], we have defined the concepts of lacunary statistical convergence of order ? and strong N?(p)-summability of order ? for sequences of complex (or real) numbers. In this paper we continue to examine others relations between lacunary statistical convergence of order ? and strong N?(p)-summability of order ?.

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46

Ulusu, Uğur, and Fatih Nuray. "On Asymptotically Lacunary Statistical Equivalent Set Sequences." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/310438.

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This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence. In addition, we also present asymptotically equivalent (Wijsman sense) analogs of theorems in Patterson and Savaş (2006).

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47

de la Rosa, María del Pilar Romero. "On Modulated Lacunary Statistical Convergence of Double Sequences." Mathematics 11, no. 4 (2023): 1042. http://dx.doi.org/10.3390/math11041042.

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Abstract:

In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function f (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this paper, we will explore such a structure in the framework of lacunary statistical convergence for double sequences and discover that such structure remains true for lacunary compatible modulus functions. Thus, we continue the work of Hacer Şenül, Mikail Et and Yavuz Altin, and we fully solve some questions posed by them.

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48

Carlos, Granados, Osu Bright O. та Das Birojit. "Neutrosophic Y-Cesàro summability of a sequence of order α, of neutrosophic random variables in probability". Annals of the University of Craiova Mathematics and Computer Science Series 50, № 2 (2023): 362–70. http://dx.doi.org/10.52846/ami.v50i2.1718.

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Abstract:

In this paper, we define the notions of neutrosophic $ \mathfrak{Y} $-Ces\`aro summability of a sequence of order $ \alpha $, neutrosophic $ \mathfrak{Y} $-lacunary statistical convergence of order $ \alpha $, neutrosophic strongly $ \mathfrak{Y} $-lacunary statistical convergence of order $ \alpha $ and neutrosophic strongly $ \mathfrak{Y} $-Ces\`aro summability of order $ \alpha $ in neutrosophic probability. Besides, we prove some relations among them.

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49

Kaya, Yusuf, and Nazmiye Gönül. "A Generalization of Lacunary Equistatistical Convergence of Positive Linear Operators." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/514174.

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Abstract:

In this paper we consider some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence. In particular we study lacunary equi-statistical convergence of approximating operators on spaces, the spaces of all real valued continuous functions de ned on and satisfying some special conditions.

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50

Srivastava, H. M., та Mikail Et. "Lacunary statistical convergence and strongly lacunary summable functions of order α". Filomat 31, № 6 (2017): 1573–82. http://dx.doi.org/10.2298/fil1706573s.

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