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Journal articles on the topic 'Convergence order'

Author: Grafiati

Published: 7 July 2024

Last updated: 31 July 2025

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1

Argyros, I. K., and S. George. "Comparison between some sixth convergence order solvers." Issues of Analysis 27, no. 3 (2020): 54–65. http://dx.doi.org/10.15393/j3.art.2020.8690.

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2

AYDIN, ABDULLAH, MUHAMMED ÇINAR та MIKAIL ET. "(V, λ)-ORDER SUMMABLE IN RIESZ SPACES". Journal of Science and Arts 21, № 3 (2021): 639–48. http://dx.doi.org/10.46939/j.sci.arts-21.3-a04.

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Statistical convergence is an active area, and it appears in a wide variety of topics. However, it has not been studied extensively in Riesz spaces. There are a few studies about the statistical convergence on Riesz spaces, but they only focus on the relationship between statistical and order convergences of sequences in Riesz spaces. In this paper, we introduce the notion of (V, λ)-order summable by using the concept of λ- statistical monotone and the λ-statistical order convergent sequences in Riesz spaces. Moreover, we give some relations between (V, λ)-order summable and λ-statistical orde

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3

Khurana, Surjit Singh. "Order convergence of vector measures on topological spaces." Mathematica Bohemica 133, no. 1 (2008): 19–27. http://dx.doi.org/10.21136/mb.2008.133944.

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4

Potra, F. A. "OnQ-order andR-order of convergence." Journal of Optimization Theory and Applications 63, no. 3 (1989): 415–31. http://dx.doi.org/10.1007/bf00939805.

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5

Kaplan. "ON UNBOUNDED ORDER CONVERGENCE." Real Analysis Exchange 23, no. 1 (1997): 175. http://dx.doi.org/10.2307/44152839.

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6

van der Walt, Jan Harm. "The order convergence structure." Indagationes Mathematicae 21, no. 3-4 (2011): 138–55. http://dx.doi.org/10.1016/j.indag.2011.02.004.

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7

Fleischer, Isidore. "Order-Convergence in Posets." Mathematische Nachrichten 142, no. 1 (1989): 215–18. http://dx.doi.org/10.1002/mana.19891420114.

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8

Yihui, Zhou, and Zhao Bin. "Order-convergence and lim-infM-convergence in posets." Journal of Mathematical Analysis and Applications 325, no. 1 (2007): 655–64. http://dx.doi.org/10.1016/j.jmaa.2006.02.016.

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9

Beyer, W. A., B. R. Ebanks, and C. R. Qualls. "Convergence rates and convergence-order profiles for sequences." Acta Applicandae Mathematicae 20, no. 3 (1990): 267–84. http://dx.doi.org/10.1007/bf00049571.

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10

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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11

Anguelov, Roumen, and Jan Harm van der Walt. "Order convergence structure onC(X)." Quaestiones Mathematicae 28, no. 4 (2005): 425–57. http://dx.doi.org/10.2989/16073600509486139.

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12

CHRISTOFIDES, DEMETRES, and DANIEL KRÁL’. "First-Order Convergence and Roots." Combinatorics, Probability and Computing 25, no. 2 (2015): 213–21. http://dx.doi.org/10.1017/s0963548315000048.

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Nešetřil and Ossona de Mendez introduced the notion of first-order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether, if (Gi)i∈ℕ is a sequence of graphs with M being their first-order limit and v is a vertex of M, then there exists a sequence (vi)i∈ℕ of vertices such that the graphs Gi rooted at vi converge to M rooted at v. We show that this holds for almost all vertices v of M, and we give an example showing that the statement need not hold for all vertices.

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13

Abramovich, Yuri, and Gleb Sirotkin. "On Order Convergence of Nets." Positivity 9, no. 3 (2005): 287–92. http://dx.doi.org/10.1007/s11117-004-7543-x.

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14

Kardoš, František, Daniel Král’, Anita Liebenau, and Lukáš Mach. "First order convergence of matroids." European Journal of Combinatorics 59 (January 2017): 150–68. http://dx.doi.org/10.1016/j.ejc.2016.08.005.

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15

Li, Anshui, Yuanyuan Wang, and Minzhi Zhao. "On the convergence of bivariate order statistics: Almost sure convergence and convergence rate." Journal of Computational and Applied Mathematics 348 (March 2019): 445–52. http://dx.doi.org/10.1016/j.cam.2018.09.005.

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16

Wang, Zhangjun, and Zili Chen. "Applications for Unbounded Convergences in Banach Lattices." Fractal and Fractional 6, no. 4 (2022): 199. http://dx.doi.org/10.3390/fractalfract6040199.

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Several recent papers investigated unbounded convergences in Banach lattices. The focus of this paper is to apply the results of unbounded convergence to the classical Banach lattice theory from a new perspective. Combining all unbounded convergences, including unbounded order (norm, absolute weak, absolute weak*) convergence, we characterize L-weakly compact sets, L-weakly compact operators and M-weakly compact operators on Banach lattices. For applications, we introduce so-called statistical-unbounded convergence and use these convergences to describe KB-spaces and reflexive Banach lattices.

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17

Sun, Tao, and Nianbai Fan. "The Equivalence of Two Modes of Order Convergence." Mathematics 12, no. 10 (2024): 1438. http://dx.doi.org/10.3390/math12101438.

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It is well known that if a poset satisfies Property A and its dual form, then the o-convergence and o2-convergence in the poset are equivalent. In this paper, we supply an example to illustrate that a poset in which the o-convergence and o2-convergence are equivalent may not satisfy Property A or its dual form, and carry out some further investigations on the equivalence of the o-convergence and o2-convergence. By introducing the concept of the local Frink ideals (the dually local Frink ideals) and establishing the correspondence between ID-pairs and nets in a poset, we prove that the o-conver

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18

Behl, Ramandeep, Ioannis K. Argyros, and Fouad Othman Mallawi. "Some High-Order Convergent Iterative Procedures for Nonlinear Systems with Local Convergence." Mathematics 9, no. 12 (2021): 1375. http://dx.doi.org/10.3390/math9121375.

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In this study, we suggested the local convergence of three iterative schemes that works for systems of nonlinear equations. In earlier results, such as from Amiri et al. (see also the works by Behl et al., Argryos et al., Chicharro et al., Cordero et al., Geum et al., Guitiérrez, Sharma, Weerakoon and Fernando, Awadeh), authors have used hypotheses on high order derivatives not appearing on these iterative procedures. Therefore, these methods have a restricted area of applicability. The main difference of our study to earlier studies is that we adopt only the first order derivative in the conv

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19

Vural, Mehmet. "Unbounded Star Convergence in Lattices." Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7, no. 4 (2024): 1775–82. http://dx.doi.org/10.47495/okufbed.1435110.

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Let L be a vector lattice, "(" x_α ") " be a L-valued net, and x∈L . If |x_α-x|∧u→┴o 0 for every u ∈〖 L〗_+ then it is said that the net "(" x_α ")" unbounded order converges to x and is denoted by □(x_α □(→┴uo x)) . This definition of unbounded order convergence has been extensively studied on many structures, including vector lattices, local solid vector lattices, normed lattices and lattice normed spaces. It is not possible to apply this type of convergence to general lattices due to the lack of algebraic structure. Therefore, we will use a type of convergence that is considered to be the mo

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20

Debnath, Shyamal, та Bijoy Das. "Statistical Convergence of Order α for Complex Uncertain Sequences". Journal of Uncertain Systems 14, № 02 (2021): 2150012. http://dx.doi.org/10.1142/s1752890921500124.

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In this paper, we introduce convergence concepts namely, statistical convergence of order [Formula: see text], statistical convergence of order [Formula: see text] almost surely, statistical convergence of order [Formula: see text] in measure, statistical convergence of order [Formula: see text] in mean, statistical convergence of order [Formula: see text] in distribution in complex uncertain theory. We also investigate some relationships among them.

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21

LAVRIC, BORIS. "ORDER CONVERGENCE OF ORDER BOUNDED SEQUENCES IN RIESZ SPACES." Tamkang Journal of Mathematics 29, no. 1 (1998): 41–45. http://dx.doi.org/10.5556/j.tkjm.29.1998.4297.

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We consider sequences in a Dedekind $\sigma$-complete Riese space, satisfying a recursive relation \[ x_{n+p}\ge \sum_{j=1}^p \alpha_{n,j} x_{n+p-j} \qquad \text{for } n=1, 2, \cdots\] where $p$ is a given natural number and $\alpha_{n,j}$ are nonnegative real numbers satisfying $\sum_{j=1}^p\alpha_{n,j}=1$. We obtain a sufficient condition on coefficients $\alpha_{n,j}$ for which order boundedness of such a sequence $(x_n)_{n=1}^\infty$ implies its order convergence. In a particular case when $\alpha_{n,j}=\alpha_{j}$ for all $n$ and $j$, it is shown that every order bounded sequence satisfyi

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22

Şengul, Hacer, Mikail Et та Mahmut Işık. "On I-deferred statistical convergence of order α". Filomat 33, № 9 (2019): 2833–40. http://dx.doi.org/10.2298/fil1909833s.

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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 I-deferred statistical convergence of order ? and strong I-deferred Ces?ro convergence of order ? and investigated between their relationship.

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23

Riecanová, Zdenka. "Topological and order-topological orthomodular lattices." Bulletin of the Australian Mathematical Society 46, no. 3 (1992): 509–18. http://dx.doi.org/10.1017/s0004972700012168.

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The necessary and sufficient conditions for atomic orthomodular lattices to have the MacNeille completion modular, or (o)-continuous or order topological, orthomodular lattices are proved. Moreover we show that if in an orthomodular lattice the (o)-convergence of filters is topological then the (o)-convergence of nets need not be topological. Finally we show that even in the case when the MacNeille completion of an orthomodular lattice L is order-topological, then in general the (o)-convergence of nets in does not imply their (o)-convergence in L. (This disproves, also for the orthomodular and

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24

Argyros, Christopher I., Ioannis K. Argyros, Stepan Shakhno, and Halyna Yarmola. "On the Semi-Local Convergence of a Fifth-Order Convergent Method for Solving Equations." Foundations 2, no. 1 (2022): 140–50. http://dx.doi.org/10.3390/foundations2010008.

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We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis, we use the approach of restricted convergence regions in combination with majorizing scalar sequences and our technique of recurrent functions. Finally, a numerical example is given.

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25

Păvăloiu, Ion. "Local convergence of general Steffensen type methods." Journal of Numerical Analysis and Approximation Theory 33, no. 1 (2004): 79–86. http://dx.doi.org/10.33993/jnaat331-762.

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We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence order of the classical Steffensen method. The convergence order of our method is greater or equal to the number of the controlled nodes used in the Lagrange-type inverse interpolation, which, in its turn, is substantially higher than the convergence orders of the Lagrange type inverse interpolation with uncontrolled nodes (since their convergence order is at most \(2\)).

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26

Guseinov, S. "CONVERGENCE ORDER OF ONE REGULARIZATION METHOD." Mathematical Modelling and Analysis 8, no. 1 (2003): 25–32. http://dx.doi.org/10.3846/13926292.2003.9637207.

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The multiscale solution of the Klein‐Gordon equations in the linear theory of (two‐phase) materials with microstructure is defined by using a family of wavelets based on the harmonic wavelets. The connection coefficients are explicitly computed and characterized by a set of differential equations. Thus the propagation is considered as a superposition of wavelets at different scale of approximation, depending both on the physical parameters and on the connection coefficients of each scale. The coarse level concerns with the basic harmonic trend while the small details, arising at more refined l

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27

Karakaş, Abdulkadir, Yavuz Altın та Mikail Et. "Δmp - statistical convergence of order α". Filomat 32, № 16 (2018): 5565–72. http://dx.doi.org/10.2298/fil1816565k.

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In this work, we generalize the concepts of statistically convergent sequence of order ? and statistical Cauchy sequence of order ? by using the generalized difference operator ?m. We prove that a sequence is ?mp-statistically convergent of order ? if and only if it is ?mp-statistically Cauchy of order ?.

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28

Conti, C., and K. Jetter. "Concerning Order of Convergence for Subdivision." Numerical Algorithms 36, no. 4 (2004): 345–63. http://dx.doi.org/10.1007/s11075-004-3896-2.

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29

Grimmett, Geoffrey. "Weak convergence using higher-order cumulants." Journal of Theoretical Probability 5, no. 4 (1992): 767–73. http://dx.doi.org/10.1007/bf01058728.

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30

Çolak, R., та Ç. A. Bektaş. "λ-Statistical convergence of order α". Acta Mathematica Scientia 31, № 3 (2011): 953–59. http://dx.doi.org/10.1016/s0252-9602(11)60288-9.

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31

Gao, Niushan. "Unbounded order convergence in dual spaces." Journal of Mathematical Analysis and Applications 419, no. 1 (2014): 347–54. http://dx.doi.org/10.1016/j.jmaa.2014.04.067.

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32

Smith, Hal L., and Horst R. Thieme. "Convergence for Strongly Order-Preserving Semiflows." SIAM Journal on Mathematical Analysis 22, no. 4 (1991): 1081–101. http://dx.doi.org/10.1137/0522070.

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33

Denk, Robert. "Filter Functions with Exponential Convergence Order." Mathematische Nachrichten 169, no. 1 (2006): 107–15. http://dx.doi.org/10.1002/mana.19941690110.

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34

Xue, Xuemei, and Jian Tao. "Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces." Journal of Function Spaces 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/9092136.

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A new concept of statistically e-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statistically e-uniform Cauchy sequences, these three kinds of convergence for sequences coincide. Moreover, we show that the statistical order convergence and the statistically relatively uniform convergence need not be equivalent. Finally, we prove that, for monotone sequences in Banach lattices, the norm statistical convergence coincides with the weak statistical conv

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35

Ren, Hongmin, and Qingbiao Wu. "Convergence ball of a modified secant method with convergence order 1.839…" Applied Mathematics and Computation 188, no. 1 (2007): 281–85. http://dx.doi.org/10.1016/j.amc.2006.09.111.

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36

Argyros, Ioannis K., and Santhosh George. "Local convergence of a fifth convergence order method in Banach space." Arab Journal of Mathematical Sciences 23, no. 2 (2017): 205–14. http://dx.doi.org/10.1016/j.ajmsc.2016.10.002.

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37

Zhang, Xin, Yu Bo, and Yuanfeng Jin. "A Temporal Second-Order Difference Scheme for Variable-Order-Time Fractional-Sub-Diffusion Equations of the Fourth Order." Fractal and Fractional 8, no. 2 (2024): 112. http://dx.doi.org/10.3390/fractalfract8020112.

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In this article, we develop a compact finite difference scheme for a variable-order-time fractional-sub-diffusion equation of a fourth-order derivative term via order reduction. The proposed scheme exhibits fourth-order convergence in space and second-order convergence in time. Additionally, we provide a detailed proof for the existence and uniqueness, as well as the stability of scheme, along with a priori error estimates. Finally, we validate our theoretical results through various numerical computations.

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38

Wang, Zhangjun, and Zili Chen. "Continuous Operators for Unbounded Convergence in Banach Lattices." Mathematics 10, no. 6 (2022): 966. http://dx.doi.org/10.3390/math10060966.

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Recently, continuous functionals for unbounded order (norm, weak and weak*) in Banach lattices were studied. In this paper, we study the continuous operators with respect to unbounded convergences. We first investigate the approximation property of continuous operators for unbounded convergence. Then we show some characterizations of the continuity of the continuous operators for uo, un, uaw and uaw*-convergence. Based on these results, we discuss the order-weakly compact operators on Banach lattices.

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39

Barrada, Mohammed, Mariya Ouaissa, Yassine Rhazali, and Mariyam Ouaissa. "A New Class of Halley’s Method with Third-Order Convergence for Solving Nonlinear Equations." Journal of Applied Mathematics 2020 (July 2, 2020): 1–13. http://dx.doi.org/10.1155/2020/3561743.

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In this paper, we present a new family of methods for finding simple roots of nonlinear equations. The convergence analysis shows that the order of convergence of all these methods is three. The originality of this family lies in the fact that these sequences are defined by an explicit expression which depends on a parameter p where p is a nonnegative integer. A first study on the global convergence of these methods is performed. The power of this family is illustrated analytically by justifying that, under certain conditions, the method convergence’s speed increases with the parameter p. This

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40

Gok, Omer. "On collectively multiplicative order convergence on the lattice ordered algebras." International Mathematical Forum 19, no. 2 (2024): 101–6. https://doi.org/10.12988/imf.2024.914480.

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41

Zhang, Kuanqiao, and Suochang Yang. "Second-Order Sliding Mode Guidance Law considering Second-Order Dynamics of Autopilot." Journal of Control Science and Engineering 2019 (June 9, 2019): 1–11. http://dx.doi.org/10.1155/2019/8573140.

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Aiming at the requirement that some missiles need to meet certain impact angles when attacking targets, we consider the second-order dynamic characteristics of autopilot, thereby proposing a second-order sliding mode guidance law with impact angle constraint. Firstly, based on the terminal sliding mode control, we design a fast nonsingular terminal sliding mode guidance law with impact angle constraint. Based on the second-order sliding mode control, a second-order sliding mode guidance law with impact angle constraint is proposed. We have proved its finite time convergence characteristics and

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42

Das, Bijoy, та Chiranjib Choudhury. "ON I-DEFERRED STATISTICAL CONVERGENCE OF ORDER Α FOR COMPLEX UNCERTAIN SEQUENCES". Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 16, № 2 (2024): 214–26. http://dx.doi.org/10.56082/annalsarscimath.2024.2.214.

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In this paper, we introduce the concepts of I-deferred statistical convergence almost surely of order α, I-deferred statistical convergence in measure of order α, I-deferred statistical convergence in mean of order α, I-deferred statistical convergence in distribution of order α, I-deferred statistical convergence in uniformly almost surely of order α and some relationships among them are discussed.

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43

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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44

Sadananda, Ramya, Santhosh George, Ioannis K. Argyros, and Jidesh Padikkal. "Order of Convergence and Dynamics of Newton–Gauss-Type Methods." Fractal and Fractional 7, no. 2 (2023): 185. http://dx.doi.org/10.3390/fractalfract7020185.

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On the basis of the new iterative technique designed by Zhongli Liu in 2016 with convergence orders of three and five, an extension to order six can be found in this paper. The study of high-convergence-order iterative methods under weak conditions is of extreme importance, because higher order means that fewer iterations are carried out to achieve a predetermined error tolerance. In order to enhance the practicality of these methods by Zhongli Liu, the convergence analysis is carried out without the application of Taylor expansion and requires the operator to be only two times differentiable,

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45

Argyros, Ioannis K., Debasis Sharma, Christopher I. Argyros, and Sanjaya Kumar Parhi. "Extending the Local Convergence of a Seventh Convergence Order Method without Derivatives." Foundations 2, no. 2 (2022): 338–47. http://dx.doi.org/10.3390/foundations2020023.

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For the purpose of obtaining solutions to Banach-space-valued nonlinear models, we offer a new extended analysis of the local convergence result for a seventh-order iterative approach without derivatives. Existing studies have used assumptions up to the eighth derivative to demonstrate its convergence. However, in our convergence theory, we only use the first derivative. Thus, in contrast to previously derived results, we obtain conclusions on calculable error estimates, convergence radius, and uniqueness region for the solution. As a result, we are able to broaden the utility of this efficien

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46

Maxwell, James, Jianliang Tong, and Clifton M. Schor. "The first and second order dynamics of accommodative convergence and disparity convergence." Vision Research 50, no. 17 (2010): 1728–39. http://dx.doi.org/10.1016/j.visres.2010.05.029.

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47

Kumar, Sunil, Janak Raj Sharma, Ioannis K. Argyros, and Samundra Regmi. "Three-Step Derivative-Free Method of Order Six." Foundations 3, no. 3 (2023): 573–88. http://dx.doi.org/10.3390/foundations3030034.

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Derivative-free iterative methods are useful to approximate the numerical solutions when the given function lacks explicit derivative information or when the derivatives are too expensive to compute. Exploring the convergence properties of such methods is crucial in their development. The convergence behavior of such approaches and determining their practical applicability require conducting local as well as semi-local convergence analysis. In this study, we explore the convergence properties of a sixth-order derivative-free method. Previous local convergence studies assumed the existence of d

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48

Aktuğlu, Hüseyin, та Halil Gezer. "Korovkin type approximation theorems proved viaweighted αβ-equistatistical convergence for bivariate functions". Filomat 32, № 18 (2018): 6253–66. http://dx.doi.org/10.2298/fil1818253a.

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Statistical convergence was extended to weighted statistical convergence in [24], by using a sequence of real numbers sk, satisfying some conditions. Later, weighted statistical convergence was considered in [35] and [19] with modified conditions on sk. Weighted statistical convergence is an extension of statistical convergence in the sense that, for sk = 1, for all k, it reduces to statistical convergence. A definition of weighted ??-statistical convergence of order ?, considered in [25] does not have this property. To remove this extension problem the definition given in [25] needs some modi

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49

Çolak, R., and Y. Altin. "Statistical Convergence of Double Sequences of Order." Journal of Function Spaces and Applications 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/682823.

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We intend to make a new approach and introduce the concepts of statistical convergence of order and strongly -Cesàro summability of order for double sequences of complex or real numbers. Also, some relations between the statistical convergence of order and strong -Cesàro summability of order are given.

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50

Temizsu, Fatih, Mikail Et та Muhammed Çinar. "Δm-deferred statistical convergence of order α". Filomat 30, № 3 (2016): 667–73. http://dx.doi.org/10.2298/fil1603667t.

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In this paper, we introduce the concepts of ?m-deferred statistical convergence of order ? and strong ?mr-deferred Ces?ro summability of order ? of real sequences. Additionally, some inclusion relations about ?m-deferred statistical convergence of order ? and strong ?mr-deferred Ces?ro summability of order ? are given.

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