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Artykuły w czasopismach na temat „Convergence order”

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Autor: Grafiati

Data publikacji: 7 lipca 2024

Data aktualizacji: 7 lipca 2024

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1

AYDIN, ABDULLAH, MUHAMMED ÇINAR i MIKAIL ET. "(V, λ)-ORDER SUMMABLE IN RIESZ SPACES". Journal of Science and Arts 21, nr 3 (30.09.2021): 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 order convergence.

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2

Argyros, I. K., i S. George. "Comparison between some sixth convergence order solvers". Issues of Analysis 27, nr 3 (listopad 2020): 54–65. http://dx.doi.org/10.15393/j3.art.2020.8690.

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3

Khurana, Surjit Singh. "Order convergence of vector measures on topological spaces". Mathematica Bohemica 133, nr 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, nr 3 (grudzień 1989): 415–31. http://dx.doi.org/10.1007/bf00939805.

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5

Ebrahimzadeh, Masoumeh, i Kazem Haghnejad Azar. "Unbounded Order Convergence in Ordered Vector Spaces". Journal of Mathematics 2024 (29.04.2024): 1–6. http://dx.doi.org/10.1155/2024/9960246.

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We consider an ordered vector space X. We define the net xα⊆X to be unbounded order convergent to x (denoted as xα⟶uox). This means that for every 0≤y∈X, there exists a net yβ (potentially over a different index set) such that yβ↓0, and for every β, there exists α0 such that ±xα−xu,yl⊆yβl whenever α≥α0. The emergence of a broader convergence, stemming from the recognition of more ordered vector spaces compared to lattice vector spaces, has prompted an expansion and broadening of discussions surrounding lattices to encompass additional spaces. We delve into studying the properties of this convergence and explore its relationships with other established order convergence. In every ordered vector space, we demonstrate that under certain conditions, every uo-convergent net implies uo-Cauchy, and vice versa. Let X be an order dense subspace of the directed ordered vector space Y. If J⊆Y is a uo-band in Y, then we establish that J∩X is a uo-band in X.

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6

Kaplan. "ON UNBOUNDED ORDER CONVERGENCE". Real Analysis Exchange 23, nr 1 (1997): 175. http://dx.doi.org/10.2307/44152839.

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7

van der Walt, Jan Harm. "The order convergence structure". Indagationes Mathematicae 21, nr 3-4 (sierpień 2011): 138–55. http://dx.doi.org/10.1016/j.indag.2011.02.004.

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8

Fleischer, Isidore. "Order-Convergence in Posets". Mathematische Nachrichten 142, nr 1 (1989): 215–18. http://dx.doi.org/10.1002/mana.19891420114.

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9

Yihui, Zhou, i Zhao Bin. "Order-convergence and lim-infM-convergence in posets". Journal of Mathematical Analysis and Applications 325, nr 1 (styczeń 2007): 655–64. http://dx.doi.org/10.1016/j.jmaa.2006.02.016.

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10

Beyer, W. A., B. R. Ebanks i C. R. Qualls. "Convergence rates and convergence-order profiles for sequences". Acta Applicandae Mathematicae 20, nr 3 (wrzesień 1990): 267–84. http://dx.doi.org/10.1007/bf00049571.

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11

Boccuto, Antonio, i Pratulananda Das. "On matrix methods of convergence of order α in (ℓ)-groups". Filomat 29, nr 9 (2015): 2069–77. http://dx.doi.org/10.2298/fil1509069b.

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We introduce a concept of convergence of order ?, with 0 < ? ? 1, with respect to a summability matrix method A for sequences (which generalizes the notion of statistical convergence of order ?), taking values in (?)-groups. Some main properties and differences with the classical A-convergence are investigated. A Cauchy-type criterion and a closedness result for the space of convergent sequences according our notion is proved.

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12

Antal, Reena, Meenakshi Chawla i Vijay Kumar. "SOME REMARKS ON ROUGH STATISTICAL \(\Lambda\)-CONVERGENCE OF ORDER \(\alpha\)". Ural Mathematical Journal 7, nr 1 (30.07.2021): 16. http://dx.doi.org/10.15826/umj.2021.1.002.

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The main purpose of this work is to define Rough Statistical \(\Lambda\)-Convergence of order \(\alpha\) \((0<\alpha\leq1)\) in normed linear spaces. We have proved some basic properties and also provided some examples to show that this method of convergence is more generalized than the rough statistical convergence. Further, we have shown the results related to statistically \(\Lambda\)-bounded sets of order \(\alpha\) and sets of rough statistically \(\Lambda\)-convergent sequences of order \(\alpha\).

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13

AYDIN, ABDULLAH. "THE CONVERGENCE ON ALGEBRAIC LATTICE NORMED SPACES". Journal of Science and Arts 20, nr 4 (30.12.2020): 909–16. http://dx.doi.org/10.46939/j.sci.arts-20.4-a11.

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The multiplicative convergence on Riesz algebras introduced and investigated with respect to norm and order convergences. If X is a Riesz space and E is a Riesz algebra then the vector norm μ:X→E_+ can be considered. Then (X,μ,E) is called algebraic lattice normed spaces. A net (x_α )_(α∈A) in an (X,μ,E) is said to be multiplicative μ-convergent to x∈X if μ(x_α-x)∙u□(→┴o ) 0 holds for all u∈E_+. In this paper, the general properties of this convergence are studied.

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14

Hu, Yibo, Qi Wu, Shuai Ma, Tianxiao Ma, Lei Shan, Xiao Wang, Yonggang Nie i in. "Comparative genomics reveals convergent evolution between the bamboo-eating giant and red pandas". Proceedings of the National Academy of Sciences 114, nr 5 (17.01.2017): 1081–86. http://dx.doi.org/10.1073/pnas.1613870114.

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Phenotypic convergence between distantly related taxa often mirrors adaptation to similar selective pressures and may be driven by genetic convergence. The giant panda (Ailuropoda melanoleuca) and red panda (Ailurus fulgens) belong to different families in the order Carnivora, but both have evolved a specialized bamboo diet and adaptive pseudothumb, representing a classic model of convergent evolution. However, the genetic bases of these morphological and physiological convergences remain unknown. Through de novo sequencing the red panda genome and improving the giant panda genome assembly with added data, we identified genomic signatures of convergent evolution. Limb development genesDYNC2H1andPCNThave undergone adaptive convergence and may be important candidate genes for pseudothumb development. As evolutionary responses to a bamboo diet, adaptive convergence has occurred in genes involved in the digestion and utilization of bamboo nutrients such as essential amino acids, fatty acids, and vitamins. Similarly, the umami taste receptor geneTAS1R1has been pseudogenized in both pandas. These findings offer insights into genetic convergence mechanisms underlying phenotypic convergence and adaptation to a specialized bamboo diet.

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15

Bao, Chunhui, Yifei Pu i Yi Zhang. "Fractional-Order Deep Backpropagation Neural Network". Computational Intelligence and Neuroscience 2018 (3.07.2018): 1–10. http://dx.doi.org/10.1155/2018/7361628.

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In recent years, the research of artificial neural networks based on fractional calculus has attracted much attention. In this paper, we proposed a fractional-order deep backpropagation (BP) neural network model with L2 regularization. The proposed network was optimized by the fractional gradient descent method with Caputo derivative. We also illustrated the necessary conditions for the convergence of the proposed network. The influence of L2 regularization on the convergence was analyzed with the fractional-order variational method. The experiments have been performed on the MNIST dataset to demonstrate that the proposed network was deterministically convergent and can effectively avoid overfitting.

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16

Ilic, Snezana, i Lidija Rancic. "On the fourth order zero-finding methods for polynomials". Filomat, nr 17 (2003): 35–46. http://dx.doi.org/10.2298/fil0317035i.

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The fourth order methods for the simultaneous approximation of simple complex zeros of a polynomial are considered. The main attention is devoted to a new method that may be regarded as a modification of the well known cubically convergent Ehrlich-Aberth method. It is proved that this method has the order of convergence equals four. Two numerical examples are given to demonstrate the convergence behavior of the studied methods.

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17

Du, Rui, Zhao-peng Hao i Zhi-zhong Sun. "Lubich Second-Order Methods for Distributed-Order Time-Fractional Differential Equations with Smooth Solutions". East Asian Journal on Applied Mathematics 6, nr 2 (maj 2016): 131–51. http://dx.doi.org/10.4208/eajam.020615.030216a.

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AbstractThis article is devoted to the study of some high-order difference schemes for the distributed-order time-fractional equations in both one and two space dimensions. Based on the composite Simpson formula and Lubich second-order operator, a difference scheme is constructed with convergence in the L1(L∞)-norm for the one-dimensional case, where τ,h and σ are the respective step sizes in time, space and distributed-order. Unconditional stability and convergence are proven. An ADI difference scheme is also derived for the two-dimensional case, and proven to be unconditionally stable and convergent in the L1(L∞)-norm, where h1 and h2 are the spatial step sizes. Some numerical examples are also given to demonstrate our theoretical results.

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18

Yi, Taishan, i Xingfu Zou. "Generic Quasi-Convergence for Essentially Strongly Order-Preserving Semiflows". Canadian Mathematical Bulletin 52, nr 2 (1.06.2009): 315–20. http://dx.doi.org/10.4153/cmb-2009-034-7.

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AbstractBy employing the limit set dichotomy for essentially strongly order-preserving semiflows and the assumption that limit sets have infima and suprema in the state space, we prove a generic quasi-convergence principle implying the existence of an open and dense set of stable quasi-convergent points. We also apply this generic quasi-convergence principle to a model for biochemical feedback in protein synthesis and obtain some results about the model which are of theoretical and realistic significance.

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19

Vaarmann, Otu. "HIGH ORDER ITERATIVE METHODS FOR DECOMPOSITION‐COORDINATION PROBLEMS". Technological and Economic Development of Economy 12, nr 1 (31.03.2006): 56–61. http://dx.doi.org/10.3846/13928619.2006.9637723.

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Many real‐life optimization problems are of the multiobjective type and highdimensional. Possibilities for solving large scale optimization problems on a computer network or multiprocessor computer using a multi‐level approach are studied. The paper treats numerical methods in which procedural and rounding errors are unavoidable, for example, those arising in mathematical modelling and simulation. For the solution of involving decomposition‐coordination problems some rapidly convergent interative methods are developed based on the classical cubically convergent method of tangent hyperbolas (Chebyshev‐Halley method) and the method of tangent parabolas (Euler‐Chebyshev method). A family of iterative methods having the convergence order equal to four is also considered. Convergence properties and computational aspects of the methods under consideration are examined. The problems of their global implementation and polyalgorithmic strategy are discussed as well.

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20

Anguelov, Roumen, i Jan Harm van der Walt. "Order convergence structure onC(X)". Quaestiones Mathematicae 28, nr 4 (grudzień 2005): 425–57. http://dx.doi.org/10.2989/16073600509486139.

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21

CHRISTOFIDES, DEMETRES, i DANIEL KRÁL’. "First-Order Convergence and Roots". Combinatorics, Probability and Computing 25, nr 2 (24.02.2015): 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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22

Abramovich, Yuri, i Gleb Sirotkin. "On Order Convergence of Nets". Positivity 9, nr 3 (wrzesień 2005): 287–92. http://dx.doi.org/10.1007/s11117-004-7543-x.

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23

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

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24

SENGUL, HACER, i MIKAIL ET. "Lacunary statistical convergence of order (α, β) in topological groups". Creative Mathematics and Informatics 26, nr 3 (2017): 339–44. http://dx.doi.org/10.37193/cmi.2017.03.11.

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In this paper, the concept of lacunary statistical convergence of order (α, β) is generalized to topological groups, and some inclusion relations between the set of all statistically convergent sequences of order (α, β) and the set of all lacunary statistically convergent sequences of order (α, β) are given.

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25

Hemker, Pieter W., Grigorii I. Shishkin i Lidia P. Shishkina. "High-order Time-accurate Schemes for Singularly Perturbed Parabolic Convection-diffusion Problems with Robin Boundary Conditions". Computational Methods in Applied Mathematics 2, nr 1 (2002): 3–25. http://dx.doi.org/10.2478/cmam-2002-0001.

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AbstractThe boundary-value problem for a singularly perturbed parabolic PDE with convection is considered on an interval in the case of the singularly perturbed Robin boundary condition; the highest space derivatives in the equation and in the boundary condition are multiplied by the perturbation parameter ε. The order of convergence for the known ε-uniformly convergent schemes does not exceed 1. In this paper, using a defect correction technique, we construct ε-uniformly convergent schemes of highorder time-accuracy. The efficiency of the new defect-correction schemes is confirmed by numerical experiments. A new original technigue for experimental studying of convergence orders is developed for the cases where the orders of convergence in the x-direction and in the t-direction can be substantially different.

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26

Aral, Nazlım Deniz. "Generalized lacunary statistical convergence of order β of difference sequences of fractional order". Boletim da Sociedade Paranaense de Matemática 41 (24.12.2022): 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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27

Duca, Dorel I., i Andrei Vernescu. "On the convergence rates of pairs of adjacent sequences". Journal of Numerical Analysis and Approximation Theory 49, nr 1 (8.09.2020): 45–53. http://dx.doi.org/10.33993/jnaat491-1221.

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In this paper we give a suitable definition for the pairs of adjacent (convergent) sequences of real numbers, we present some two-sided estimations which caracterize the order of convergence to its limits of some of these sequences and we give certain general explanations for its similar orders of convergence.

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28

Громов, А. Н. "On Koenig's theorem for integer functions of finite order". Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), nr 3 (12.07.2020): 280–89. http://dx.doi.org/10.26089/nummet.v21r324.

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Показано, что теорема Кенига о нулях аналитической функции, примененная к логарифмической производной целой функции конечного порядка, приводит к алгоритму отыскания нулей, для которого областями сходимости являются многоугольники Вороного искомых нулей. Так как диаграмма Вороного последовательности нулей составляет множество меры нуль, то алгоритм имеет глобальную сходимость. Дана оценка скорости сходимости. Для итераций высших порядков, которые строятся с помощью теоремы Кенига, рассмотрено влияние кратности корня на область сходимости и приводится оценка скорости сходимости. It is shown that Koenig's theorem on zeros of analytic functions applied to the logarithmic derivative of an integer function of finite order leads to an algorithm of finding zeros whose convergence domains are the Voronoi polygons of the zeros to be found. Since the Voronoi diagram of a sequence of zeros is a set of measure zero, this algorithm is globally convergent. The rate of convergence is estimated. For higher-order iterations that are constructed using Koenig's theorem, the effect of root multiplicity on the convergence domain is considered and the convergence rate is estimated for this case.

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29

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

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30

Hendy, A. S., R. H. De Staelen, A. A. Aldraiweesh i M. A. Zaky. "High order approximation scheme for a fractional order coupled system describing the dynamics of rotating two-component Bose-Einstein condensates". AIMS Mathematics 8, nr 10 (2023): 22766–88. http://dx.doi.org/10.3934/math.20231160.

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<abstract><p>A coupled system of fractional order Gross-Pitaevskii equations is under consideration in which the time-fractional derivative is given in Caputo sense and the spatial fractional order derivative is of Riesz type. This kind of model may shed light on some time-evolution properties of the rotating two-component Bose¢ Einstein condensates. An unconditional convergent high-order scheme is proposed based on L2-$ 1_{\sigma} $ finite difference approximation in the time direction and Galerkin Legendre spectral approximation in the space direction. This combined scheme is designed in an easy algorithmic style. Based on ideas of discrete fractional Grönwall inequalities, we can prove the convergence theory of the scheme. Accordingly, a second order of convergence and a spectral convergence order in time and space, respectively, without any constraints on temporal meshes and the specified degree of Legendre polynomials $ N $. Some numerical experiments are proposed to support the theoretical results.</p></abstract>

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31

Argyros, Ioannis K., Jai Prakash Jaiswal, Akanksha Saxena i Michael I. Argyros. "On the Semi-Local Convergence of a Noor–Waseem-like Method for Nonlinear Equations". Foundations 2, nr 2 (20.06.2022): 512–22. http://dx.doi.org/10.3390/foundations2020034.

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The significant feature of this paper is that the semi-local convergence of high order methods for solving nonlinear equations defined on abstract spaces has not been studied extensively as done for the local convergence by a plethora of authors which is certainly a more interesting case. A process is developed based on majorizing sequences and the notion of restricted Lipschitz condition to provide a semi-local convergence analysis for the third convergent order Noor–Waseem method. Due to the generality of our technique, it can be used on other high order methods. The convergence analysis is enhanced. Numerical applications complete are used to test the convergence criteria.

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32

Cvetkovic, Bosko, i Mihailo Lazarevic. "Fractional-order iterative learning control for robotic Arm-PD2Dα type". Filomat 35, nr 1 (2021): 1–10. http://dx.doi.org/10.2298/fil2101001c.

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In this paper, a new open-loop PD2D? type a fractional order iterative learning control (ILC) is studied for joint space trajectory tracking control of a linearized uncertain robotic arm. The robust convergent analysis of the tracking errors has been done in time domain where it is theoretically proven that the boundednesses of the tracking error are guaranteed in the presence of model uncertainty. The convergence of the proposed open-loop ILC law is proven mathematically using Gronwall integral inequality for a linearized robotic system and sufficient conditions for convergence and robustness are obtained.

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33

Wang, Zhangjun, i Zili Chen. "Applications for Unbounded Convergences in Banach Lattices". Fractal and Fractional 6, nr 4 (1.04.2022): 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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34

Artidiello, Santiago, Alicia Cordero, Juan R. Torregrosa i María P. Vassileva. "Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure". Abstract and Applied Analysis 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/289029.

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We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points.

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35

Sun, Tao, i Nianbai Fan. "The Equivalence of Two Modes of Order Convergence". Mathematics 12, nr 10 (7.05.2024): 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-convergence and o2-convergence of nets in a poset are equivalent if and only if the poset is ID-doubly continuous. This result gives a complete solution to the problem of E.S. Wolk in two modes of order convergence, which states under what conditions for a poset the o-convergence and o2-convergence in the poset are equivalent.

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36

LAVRIC, BORIS. "ORDER CONVERGENCE OF ORDER BOUNDED SEQUENCES IN RIESZ SPACES". Tamkang Journal of Mathematics 29, nr 1 (1.03.1998): 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 satisfying the above recursive relation order converges if and only if natural numbers $j \le p$ for which $\alpha_{j}>0$, are relative prime.

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37

Behl, Ramandeep, Ioannis K. Argyros i Fouad Othman Mallawi. "Some High-Order Convergent Iterative Procedures for Nonlinear Systems with Local Convergence". Mathematics 9, nr 12 (14.06.2021): 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 convergence order (which only appears on the proposed iterative procedure). No work has been proposed on computable error distances and uniqueness in the aforementioned studies given on Rk. We also address these problems too. Moreover, by using Banach space, the applicability of iterative procedures is extended even further. We have examined the convergence criteria on several real life problems along with a counter problem that completes this study.

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38

Guseinov, S. "CONVERGENCE ORDER OF ONE REGULARIZATION METHOD". Mathematical Modelling and Analysis 8, nr 1 (31.03.2003): 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 levels, describe small oscillations around the harmonic zero‐scale approximation.

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39

Karakaş, Abdulkadir, Yavuz Altın i Mikail Et. "Δmp - statistical convergence of order α". Filomat 32, nr 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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40

Conti, C., i K. Jetter. "Concerning Order of Convergence for Subdivision". Numerical Algorithms 36, nr 4 (sierpień 2004): 345–63. http://dx.doi.org/10.1007/s11075-004-3896-2.

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Grimmett, Geoffrey. "Weak convergence using higher-order cumulants". Journal of Theoretical Probability 5, nr 4 (październik 1992): 767–73. http://dx.doi.org/10.1007/bf01058728.

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Çolak, R., i Ç. A. Bektaş. "λ-Statistical convergence of order α". Acta Mathematica Scientia 31, nr 3 (maj 2011): 953–59. http://dx.doi.org/10.1016/s0252-9602(11)60288-9.

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43

Gao, Niushan. "Unbounded order convergence in dual spaces". Journal of Mathematical Analysis and Applications 419, nr 1 (listopad 2014): 347–54. http://dx.doi.org/10.1016/j.jmaa.2014.04.067.

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44

Smith, Hal L., i Horst R. Thieme. "Convergence for Strongly Order-Preserving Semiflows". SIAM Journal on Mathematical Analysis 22, nr 4 (lipiec 1991): 1081–101. http://dx.doi.org/10.1137/0522070.

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45

Denk, Robert. "Filter Functions with Exponential Convergence Order". Mathematische Nachrichten 169, nr 1 (11.11.2006): 107–15. http://dx.doi.org/10.1002/mana.19941690110.

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Sharma, Janak Raj, Ioannis K. Argyros i Deepak Kumar. "Design and Analysis of a New Class of Derivative-Free Optimal Order Methods for Nonlinear Equations". International Journal of Computational Methods 15, nr 03 (25.04.2018): 1850010. http://dx.doi.org/10.1142/s021987621850010x.

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We develop a general class of derivative free iterative methods with optimal order of convergence in the sense of Kung–Traub hypothesis for solving nonlinear equations. The methods possess very simple design, which makes them easy to remember and hence easy to implement. The Methodology is based on quadratically convergent Traub–Steffensen scheme and further developed by using Padé approximation. Local convergence analysis is provided to show that the iterations are locally well defined and convergent. Numerical examples are provided to confirm the theoretical results and to show the good performance of new methods.

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47

Şengul, Hacer, Mikail Et i Mahmut Işık. "On I-deferred statistical convergence of order α". Filomat 33, nr 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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48

Zafar, Fiza, i Gulshan Bibi. "A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations". Chinese Journal of Mathematics 2014 (29.01.2014): 1–7. http://dx.doi.org/10.1155/2014/313691.

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We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving a specific step which when combined with any two-step iterative method raises the convergence order by n+10, if n is the order of convergence of the two-step iterative method. This new class include four evaluations of function and one evaluation of the first derivative per iteration. Therefore, the efficiency index of this family is 141/5 =1.695218203. Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.

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49

Riecanová, Zdenka. "Topological and order-topological orthomodular lattices". Bulletin of the Australian Mathematical Society 46, nr 3 (grudzień 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 order-topological case, one statement in G.Birkhoff's book.)

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50

Debnath, Shyamal, i Bijoy Das. "Statistical Convergence of Order α for Complex Uncertain Sequences". Journal of Uncertain Systems 14, nr 02 (czerwiec 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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