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Journal articles on the topic 'Convergence property'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

Hayase, Toshiyuki. "Monotonic Convergence Property of Turbulent Flow Solution With Central Difference and QUICK Schemes." Journal of Fluids Engineering 121, no. 2 (1999): 351–58. http://dx.doi.org/10.1115/1.2822213.

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Monotonic convergence of numerical solutions with the computational grid refinement is an essential requirement in estimating the grid-dependent uncertainty of computational fluid dynamics. If the convergence is not monotonic, the solution could be erroneously regarded as convergent at the local extremum with respect to some measure of the error. On the other hand, if the convergence is exactly monotonic, estimation methods such as Richardson extrapolation properly evaluate the uncertainty of numerical solutions. This paper deals with the characterization of numerical schemes based on the prop

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2

YOSHIDA, Katsutoshi, and Yusuke NISHIZAWA. "Convergence Property of Noise-induced Synchronization." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2007 (May 5, 2007): 7–12. http://dx.doi.org/10.5687/sss.2007.7.

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3

Borwein, Jonathan M., and Simon Fitzpatrick. "Mosco convergence and the Kadec property." Proceedings of the American Mathematical Society 106, no. 3 (1989): 843. http://dx.doi.org/10.1090/s0002-9939-1989-0969313-4.

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4

Cornea, Aurel, and Peter A. Loeb. "A Convergence Property for Conditional Expectation." Annals of Probability 17, no. 1 (1989): 353–56. http://dx.doi.org/10.1214/aop/1176991513.

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5

Holmes, Mark J., Jesús Otero, and Theodore Panagiotidis. "Climbing the property ladder: An analysis of market integration in London property prices." Urban Studies 55, no. 12 (2017): 2660–81. http://dx.doi.org/10.1177/0042098017692303.

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We investigate the long-run convergence of house prices across the London boroughs based on a pairwise unit root probabilistic testing procedure. In sharp contrast to the earlier literature, we employ a dataset that distinguishes between four different types of property in each borough. Using a quarterly dataset that spans from 1995 to 2014, we find evidence in favour of long-run convergence thereby suggesting that the great majority of London borough house prices are driven by a single common stochastic trend. In a further contribution, we offer new insights through analysing the determinants

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6

Kisi, Omer, Burak Cakal, and Mehmet Gurdal. "ON IDEAL CONVERGENCE OF SEQUENCES IN QUATERNION VALUED GENERALIZED METRIC SPACES." Journal of Mathematical Analysis 15, no. 5 (2024): 19–42. https://doi.org/10.54379/jma-2024-5-2.

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The primary objective of this study is to introduce the notion of ideal convergence in quaternion-valued generalized metric spaces. We define Iconvergence and I ∗-convergence in these spaces and establish their equivalence through the definition of property (AP). Furthermore, we introduce I-Cauchy and I ∗-Cauchy sequences, adapting classically theorems to suit quaternionvalued generalized metric spaces. We also present I-statistical convergence, I-lacunary statistical convergence, strong I-Ces`aro summability, strong Ilacunary summability, [V, λ](I)-summability, and I-λ-statistically convergen

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7

Filipów, Rafał, Nikodem Mrożek, Ireneusz Recław, and Piotr Szuca. "Ideal convergence of bounded sequences." Journal of Symbolic Logic 72, no. 2 (2007): 501–12. http://dx.doi.org/10.2178/jsl/1185803621.

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AbstractWe generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergent subsequence) on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.

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8

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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9

Kim, Sun Kuk. "GLOBAL CONVERGENCE IN CONSTRUCTION." International Journal of Strategic Property Management 14, no. 2 (2010): 87–88. http://dx.doi.org/10.3846/ijspm.2010.07.

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10

Ogundari, Kolawole. "Club convergence of crime rates in the United States of America." Journal of Criminological Research, Policy and Practice 8, no. 1 (2021): 14–27. http://dx.doi.org/10.1108/jcrpp-03-2021-0013.

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Purpose The cyclical behavior of US crime rates reflects the dynamics of crime in the country. This paper aims to investigate the US's club convergence of crime rates to provide insights into whether the crime rates increased or decreased over time. The paper also analyzes the factors influencing the probability of states converging to a particular convergence club of crime. Design/methodology/approach The analysis is based on balanced panel data from all 50 states and the district of Columbia on violent and property crime rates covering 1976–2019. This yields a cross-state panel of 2,244 obse

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11

Basim, A. Hassan, O. Dahawi Hussein, and S. Younus Azzam. "A new kind of parameter conjugate gradient for unconstrained optimization." Indonesian Journal of Electrical Engineering and Computer Science (IJEECS) 17, no. 1 (2020): 404–11. https://doi.org/10.11591/ijeecs.v17.i1.pp404-411.

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The key feature for conjugate gradient methods is a conjugate parameter optimal for solving unrestrained minimization functions. In this paper, a replacement new parameter conjugate gradient for unconstrained optimization. The sufficient descent property cleave to. The global convergence property of the new method is proved under some assumptions. Numerical results explain that the new parameter is superior in practice.

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12

Ganie, Abdul Hamid, and Dowlath Fathima. "Almost Convergence Property of Generalized Riesz Spaces." Journal of Applied Mathematics and Computation 4, no. 4 (2020): 249–53. http://dx.doi.org/10.26855/jamc.2020.12.016.

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13

Martinez-Gimenez, Felix, and John H. Lindsey II. "A Convergence Property for Infinite Arrays: 10826." American Mathematical Monthly 108, no. 9 (2001): 877. http://dx.doi.org/10.2307/2695573.

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14

Jasinski, Jakub, and Ireneusz Recław. "On spaces with the ideal convergence property." Colloquium Mathematicum 111, no. 1 (2008): 43–50. http://dx.doi.org/10.4064/cm111-1-4.

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15

Shumilova, V. V. "On one property of two-scale convergence." Differential Equations 42, no. 1 (2006): 155–57. http://dx.doi.org/10.1134/s0012266106010150.

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16

Bórquez, R. "Recurrence property and pointwise convergence of martingales." Statistics & Probability Letters 135 (April 2018): 51–53. http://dx.doi.org/10.1016/j.spl.2017.11.019.

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17

BULLOCK, BARBARA E., and ALMEIDA JACQUELINE TORIBIO. "Introduction: Convergence as an emergent property in bilingual speech." Bilingualism: Language and Cognition 7, no. 2 (2004): 91–93. http://dx.doi.org/10.1017/s1366728904001506.

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In introducing this special issue of Bilingualism: Language and Cognition, we feel it is critical to clarify what we understand ‘linguistic convergence’ to mean in the context of bilingualism, since ‘convergence’ is a technical term more readily associated with the field of language contact than with the field of bilingualism (for recent discussions of the role of convergence in contact see Thomason and Kaufman, 1988; Thomason, 2001; Myers-Scotton, 2002; Clyne, 2003; Winford, 2003). Within the language contact literature, the term invites a variety of uses. Some researchers adopt a definition

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18

Ovie, O. Francisca &. Emeke Precious Nwaoboli. "Media Convergence and Intellectual Property Rights in Nigeria: Legal and Regulatory Challenges in the Digital Age." International Journal of Sub-Saharan African Research 2, no. 4 (2024): 343–55. https://doi.org/10.5281/zenodo.14567568.

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<strong>Background</strong>: The rapid growth of digital media in Nigeria has led to significant convergence of media platforms, raising critical concerns about intellectual property rights. <strong>Objective</strong>: The objectives of the study were to examine the legal and regulatory frameworks governing media convergence and intellectual property rights in the digital age in Nigeria; assess the impact of media convergence on content creation, distribution and consumption; and identify the strategies through which for policymakers, content creators, and regulatory bodies can effectively add

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19

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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20

SHI, ZHEN-JUN, and JIE SHEN. "CONVERGENCE PROPERTY AND MODIFICATIONS OF A MEMORY GRADIENT METHOD." Asia-Pacific Journal of Operational Research 22, no. 04 (2005): 463–77. http://dx.doi.org/10.1142/s0217595905000625.

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We study properties of a modified memory gradient method, including the global convergence and rate of convergence. Numerical results show that modified memory gradient methods are effective in solving large-scale minimization problems.

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21

Buntinas, Martin, and Naza Tanović-Miller. "Strong Boundedness and Strong Convergence in Sequence Spaces." Canadian Journal of Mathematics 43, no. 5 (1991): 960–74. http://dx.doi.org/10.4153/cjm-1991-053-8.

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AbstractStrong convergence has been investigated in summability theory and Fourier analysis. This paper extends strong convergence to a topological property of sequence spaces E. The more general property of strong boundedness is also defined and examined. One of the main results shows that for an FK-space E which contains all finite sequences, strong convergence is equivalent to the invariance property E = ℓ ν0. E with respect to coordinatewise multiplication by sequences in the space ℓν0 defined in the paper. Similarly, strong boundedness is equivalent to another invariance E = ℓν.E. The res

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22

Karakuş, Mahmut, and Feyzi Başar. "On some classical properties of normed spaces via generalized vector valued almost convergence." Mathematica Slovaca 72, no. 6 (2022): 1551–66. http://dx.doi.org/10.1515/ms-2022-0106.

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Abstract Recently, the authors interested some new problems on multiplier spaces of Lorentz’ almost convergence and f λ-convergence as a generalization of almost convergence. f λ-convergence is firstly introduced by Karakuş and Başar, and used for some new characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in a normed space X and its continuous dual X *. In the present paper, we deal with f λ-convergence to have some inclusion relations between the vector valued spaces obtained from this type convergence and corresponding classical se

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23

Lorentzen, Lisa. "The closure of convergence sets for continued fractions are convergence sets." Proceedings of the Edinburgh Mathematical Society 37, no. 1 (1994): 39–46. http://dx.doi.org/10.1017/s0013091500018666.

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We prove that if Ω is a simple convergence set for continued fractions K(an/bn), then the closure of Ω is also such a convergence set. Actually, we prove more: every continued fraction K(an/bn) has a “neighbourhood” where rn>0 and sn>0, with the following property: Every continued fraction from {n} converges if and only if K(an/bn) converges.

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24

Hu, Xueping, Guohua Fang, and Dongjin Zhu. "Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence." Discrete Dynamics in Nature and Society 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/562838.

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By applying the moment inequality for asymptotically almost negatively associated (in shortAANA) random sequence and truncated method, we get the three series theorems forAANArandom variables. Moreover, a strong convergence property for the partial sums ofAANArandom sequence is obtained. In addition, we also study strong convergence property for weighted sums ofAANArandom sequence.

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25

Ekemode, Benjamin Gbolahan, and Abel Olaleye. "Convergence between direct and indirect real estate investments." Journal of Financial Management of Property and Construction 21, no. 3 (2016): 212–30. http://dx.doi.org/10.1108/jfmpc-12-2015-0040.

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Purpose This paper aimed to examine the return/risk performance of direct and indirect real estate (listed property stock) in the Nigerian real estate market and analyzed the short-term integration between the two classes of real estate assets. It also established whether investors could achieve diversification benefits by combining both assets in a portfolio. Design/methodology/approach The data utilized comprised annual returns on direct real estate calculated from the rental and capital values of 226 direct commercial properties obtained from property valuers in Lagos, Nigeria, for a period

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26

Hiai, Fumio, and Yongdo Lim. "Convergence theorems for barycentric maps." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 03 (2019): 1950016. http://dx.doi.org/10.1142/s0219025719500164.

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We first develop a theory of conditional expectations for random variables with values in a complete metric space [Formula: see text] equipped with a contractive barycentric map [Formula: see text], and then give convergence theorems for martingales of [Formula: see text]-conditional expectations. We give the Birkhoff ergodic theorem for [Formula: see text]-values of ergodic empirical measures and provide a description of the ergodic limit function in terms of the [Formula: see text]-conditional expectation. Moreover, we prove the continuity property of the ergodic limit function by finding a

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27

Dodds, P. G., T. K. Dodds, P. N. Dowling, C. J. Lennard, and F. A. Sukochev. "A uniform Kadec-Klee property for symmetric operator spaces." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 3 (1995): 487–502. http://dx.doi.org/10.1017/s0305004100073813.

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AbstractWe show that if a rearrangement invariant Banach function space E on the positive semi-axis satisfies a non-trivial lower q-estimate with constant 1 then the corresponding space E(M) of τ-measurable operators, affiliated with an arbitrary semi-finite von Neumann algebra M equipped with a distinguished faithful, normal, semi-finite trace τ, has the uniform Kadec-Klee property for the topology of local convergence in measure. In particular, the Lorentz function spaces Lq, p and the Lorentz-Schatten classes Cg, p have the UKK property for convergence locally in measure and for the weak-op

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28

Zenin, I. A. "Convergence of Artificial Intelligence and Intellectual Property Rights." Intellectual property law 1 (March 25, 2021): 4–8. http://dx.doi.org/10.18572/2072-4322-2021-1-4-8.

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The purpose is to identify and evaluate the doctrinal definitions of the concept and recommendations on ensuring the protection of the results created by AI as products of the functioning of its technologies using the norms of the current copyright, patent and other legislation. At the same time, the goal of scientific evaluation of the existing legal definitions of the concept of AI and its accompanying categories is pursued. The methodology includes methods of logical, historical, systematic and comparative legal analysis of legal definitions, methods of translation (implementation) of doctr

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29

Y., Adekunle, Ebiesuwa Seun, and Yoro R. "Stochastic Solution on Convergence Property of Quadratic Functions." Communications on Applied Electronics 5, no. 7 (2016): 10–17. http://dx.doi.org/10.5120/cae2016652317.

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30

He Keke, and Tang Zhenmin. "The Convergence Property of the Auxiliary Particle Filter." Journal of Convergence Information Technology 7, no. 17 (2012): 97–108. http://dx.doi.org/10.4156/jcit.vol7.issue17.11.

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31

MORI, TAKEHIRO, and HIDEKI KOKAME. "Convergence property of interval matrices and interval polynomials." International Journal of Control 45, no. 2 (1987): 481–84. http://dx.doi.org/10.1080/00207178708933746.

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32

Liow, Kim Hiang. "Risk-return convergence in international public property markets." Journal of Property Research 32, no. 1 (2014): 1–32. http://dx.doi.org/10.1080/09599916.2013.872693.

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33

Mizuno, Takao, Hideyuki Sugiura, Shunya Maruta, Makoto Yamauchi, and Eisuke Kita. "1915 Improvement of Convergence Property of Grammatical Evolution." Proceedings of The Computational Mechanics Conference 2013.26 (2013): _1915–1_—_1915–2_. http://dx.doi.org/10.1299/jsmecmd.2013.26._1915-1_.

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34

UEGANIWA, Takehiro, Shunsuke ISHIMITSU, Keisuke NAMEKAWA, et al. "603 Improvement of convergence property using harmonic components." Proceedings of Conference of Chugoku-Shikoku Branch 2013.51 (2013): _603–1_—_603–2_. http://dx.doi.org/10.1299/jsmecs.2013.51._603-1_.

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35

Sheu, Shey Shiung. "A convergence property of Dubins' representation of distributions." Bulletin of the Australian Mathematical Society 38, no. 1 (1988): 83–85. http://dx.doi.org/10.1017/s000497270002726x.

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Let (Xn)n≥1 be a sequence of random variables with zero means and uniformly bounded variences. Let τn be the stopping time defined on a given Brownian motion (Bt)t≥0, B0 = 0, by Dubins' method such that B(τn) has the same distribution as Xn. We prove that Xn converging to 0 in distribution implies that τn converges to 0 in probability. Examples are presented to illustrate the result is the best possible.

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36

Pu, Dingguo, and Wenci Yu. "On the convergence property of the DFP algorithm." Annals of Operations Research 24, no. 1 (1990): 175–84. http://dx.doi.org/10.1007/bf02216822.

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37

Deng, N., and Z. Chen. "Truncated nonlinear ABS algorithm and its convergence property." Computing 45, no. 2 (1990): 169–73. http://dx.doi.org/10.1007/bf02247882.

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38

Cheng, Fulin, and Tosiro Koga. "Multichannel linear prediction models and their convergence property." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 73, no. 6 (1990): 49–57. http://dx.doi.org/10.1002/ecjc.4430730606.

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39

Bjon, Sten. "The Approximation Property for Nuclear Convergence Vector Spaces." Mathematische Nachrichten 142, no. 1 (1989): 267–75. http://dx.doi.org/10.1002/mana.19891420118.

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40

Thianwan, Tanakit. "Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings." Abstract and Applied Analysis 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/745451.

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We study weak convergence of the projection type Ishikawa iteration scheme for two asymptotically nonexpansive nonself-mappings in a real uniformly convex Banach spaceEwhich has a Fréchet differentiable norm or its dualE*has the Kadec-Klee property. Moreover, weak convergence of projection type Ishikawa iterates of two asymptotically nonexpansive nonself-mappings without any condition on the rate of convergence associated with the two maps in a uniformly convex Banach space is established. Weak convergence theorem without making use of any of the Opial's condition, Kadec-Klee property, or Fréc

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41

Ankirchner, Stefan. "Monotone utility convergence." Journal of Applied Probability 43, no. 3 (2006): 622–33. http://dx.doi.org/10.1239/jap/1158784934.

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We show that the maximal expected utility satisfies a monotone continuity property with respect to increasing information. Let be a sequence of increasing filtrations converging to , and let un(x) and u∞(x) be the maximal expected utilities when investing in a financial market according to strategies adapted to and , respectively. We give sufficient conditions for the convergence un(x) → u∞(x) as n → ∞. We provide examples in which convergence does not hold. Then we consider the respective utility-based prices, πn and π∞, of contingent claims under (Gtn) and (Gt∞). We analyse to what extent πn

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42

Sekiguchi, Masaki, Emiko Ishiwata, and Yukihiko Nakata. "Convergence of a Logistic Type Ultradiscrete Model." Discrete Dynamics in Nature and Society 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/7893049.

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We derive a piecewise linear difference equation from logistic equations with time delay by ultradiscretization. The logistic equation that we consider in this paper has been shown to be globally stable in the continuous and discrete time formulations. Here, we study if ultradiscretization preserves the global stability property, analyzing the asymptotic behaviour of the obtained piecewise linear difference equation. It is shown that our piecewise linear difference equation has a threshold property concerning global attractivity of equilibria, similar to the stable logistic equations with time

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43

Pattanaik, Pradosh Kumar, Susanta Kumar Paikray, and Biplab Kumar Rath. "Local properties of fourier series via deferred Riesz mean." Boletim da Sociedade Paranaense de Matemática 41 (December 28, 2022): 1–7. http://dx.doi.org/10.5269/bspm.62309.

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The convergence of Fourier series of a function at a point depends upon the behaviour of the function in the neighborhood of that point, and it leads to the local property of Fourier series. In the proposed work, we introduce and study the absolute convergence of the deferred Riesz summability mean, and accordingly establish a new theorem on the local property of a factored Fourier series. We also suggest a direction for future researches on this subject, which are based upon the local properties of the Fourier series via basic notions of statistical absolute convergence.

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44

Chen, Chang-Pao. "L1-convergence of Fourier series." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 3 (1986): 376–90. http://dx.doi.org/10.1017/s144678870003384x.

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AbstractFor an integrable function f on T, we introduce a modified partial sum and establish its L1-convergence property. The relation between the sum and L1-convergence classes is also established. As a corollary, a new L1-convergence class is obtained. It is shown that this class covers all known L1-convergence classes.

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45

Gnat, Sebastian. "Tests for the Presence of Price Convergence on Residential Property Market in Several Districts of Szczecin in 2006–2009." Folia Oeconomica Stetinensia 16, no. 1 (2016): 186–95. http://dx.doi.org/10.1515/foli-2016-0011.

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Abstract Neighbouring local property markets are not separate realities. They influence one another and create an interrelated system of supply and demand. Some of these interrelations are convergent, while others result in contradictory trends on the markets. Convergence is a term denoting a process of some phenomena approaching its normative level. Tests for the presence of convergence help to assess if the objects under observation show resemblance in the context of the observed phenomenon, and to find out how long it takes for this resemblance to be complete. In this paper, I propose the a

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46

Lentz, Tom, and Reinhard Blutner. "Signalling games: evolutionary convergence on optimality." ZAS Papers in Linguistics 51 (January 1, 2009): 95–110. http://dx.doi.org/10.21248/zaspil.51.2009.375.

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Horn's division of pragmatic labour (Horn, 1984) is a universal property of language, and amounts to the pairing of simple meanings to simple forms, and deviant meanings to complex forms. This division makes sense, but a community of language users that do not know it makes sense will still develop it after a while, because it gives optimal communication at minimal costs. This property of the division of pragmatic labour is shown by formalising it and applying it to a simple form of signalling games, which allows computer simulations to corroborate intuitions. The division of pragmatic labour

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47

Ankirchner, Stefan. "Monotone utility convergence." Journal of Applied Probability 43, no. 03 (2006): 622–33. http://dx.doi.org/10.1017/s0021900200001984.

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We show that the maximal expected utility satisfies a monotone continuity property with respect to increasing information. Let be a sequence of increasing filtrations converging to , and let u n (x) and u ∞(x) be the maximal expected utilities when investing in a financial market according to strategies adapted to and , respectively. We give sufficient conditions for the convergence u n (x) → u ∞(x) as n → ∞. We provide examples in which convergence does not hold. Then we consider the respective utility-based prices, π n and π∞, of contingent claims under (G t n ) and (G t ∞). We analyse to wh

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48

Wang, Yachu, and Renyong Hou. "The Influence of the Convergence of Digital and Green Technologies on Regional Total Factor Productivity: Evidence from 30 Provinces in China." Sustainability 16, no. 21 (2024): 9187. http://dx.doi.org/10.3390/su16219187.

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This paper explores the development of digital and green collaboration, empirically examining both the linear and nonlinear impacts of the convergence of digital and green technologies on regional total factor productivity (TFP). Using data from 30 provinces and cities in China from 2010 to 2022, the study constructs a panel threshold model with business environment and intellectual property protection as threshold variables to investigate their roles in mediating the effects of digital–green technology convergence on regional TFP. The key findings are as follows: (1) The linear analysis revea

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49

Cui, Yunan, Paweł Foralewski, Henryk Hudzik, and Radosław Kaczmarek. "Kadec–Klee properties of Orlicz–Lorentz sequence spaces equipped with the Orlicz norm." Positivity 25, no. 4 (2021): 1273–94. http://dx.doi.org/10.1007/s11117-020-00803-4.

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AbstractThe necessary and sufficient conditions for both the Kadec–Klee property as well as the Kadec–Klee property with respect to the coordinatewise convergence in Orlicz–Lorentz sequence spaces equipped with the Orlicz norm and generated by arbitrary Orlicz functions as well as any non-increasing weight sequences are given. Moreover, for their subspaces of elements with an order continuous norm the full characterization of the Kadec–Klee property with respect to the coordinatewise convergence is presented. Some tools useful in the proofs of the main results are also provided.

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Kolancı, Saime, and Mehmet Gurdal. "On Ideal Convergence in Generalized Metric Spaces." Dera Natung Government College Research Journal 8, no. 1 (2023): 81–96. http://dx.doi.org/10.56405/dngcrj.2023.08.01.06.

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Abstract:

Our main goal in this paper is to introduce the concept of ideal convergence in G-metric spaces. We give definitions of GI-convergence and GI*-convergence in G-metric spaces. We also extend the I-convergence concept's properties to GI-convergence. Then we demonstrate that GI-convergence and GI*-convergence are equivalent by giving the property (AP) definition. Additionally we introduce GI-Cauchy and GI*-Cauchy sequences and adapt the classically stated theorems to G-metric spaces.

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