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" Advances in summability and approximation theory / "
S.A. Mohiuddine, Tuncer Acar, editors.
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BL
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| Record Number
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891453
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| Title & Author
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Advances in summability and approximation theory /\ S.A. Mohiuddine, Tuncer Acar, editors.
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| Publication Statement
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Singapore :: Springer,, [2018]
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1 online resource
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| ISBN
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9789811330766
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: 9789811330773
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: 981133076X
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: 9811330778
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9789811330766
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| Contents
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Intro; Preface; Contents; Editors and Contributors; Tauberian Conditions Under Which Convergence Follows from Statistical Summability by Weighted Means; 1 Introduction; 2 Development of Tauberian Theory for Weighted Mean Method of Summability and Its Statistical Convergence; 3 Lemmas and Main Results for Real Sequences; 3.1 Lemmas; 3.2 Main Results; 4 Lemmas and Main Results for Complex Sequences; 4.1 Lemmas; 4.2 Main Results; References; Applications of Fixed Point Theorems and General Convergence in Orthogonal Metric Spaces; 1 Introduction; 2 Orthogonal Set; 3 Orthogonal Contractions
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Approximation Properties of Chlodowsky Variant of (p, q) Szász-Mirakyan-Stancu Operators1 Introduction and Preliminaries; 2 Construction of the Operators; 3 Korovkin-Type Approximation Theorem; 4 Rate of Convergence; References; Approximation Theorems for Positive Linear Operators Associated with Hermite and Laguerre Polynomials; 1 Introduction; 1.1 Modified Szász-Mirakjan Operators; 1.2 The Poisson Integrals for Hermite and Laguerre Expansions; 1.3 The Poisson Integrals Associated with Hermite Functions; 2 Auxiliary Results; 3 Approximation Theorems; References
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Convergence Properties of Genuine Bernstein-Durrmeyer Operators1 Introduction; 2 Preliminary Results; 3 Basic Approximation Properties; 4 Rate of Convergence in Terms of the Ditzian-Totik Modulus of Smoothness; 5 Voronovskaja-Type Theorems; 6 Rate of Convergence for Functions Whose Derivative Are of Bounded Variation; 7 Numerical Results; References; Bivariate Szász-Type Operators Based on Multiple Appell Polynomials; 1 Introduction; 2 The Construction of the Operators; 3 Weighted Approximation Properties; 4 Approximation in the Space of Bögel-Continuous Functions; References
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| Abstract
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This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. The theory of approximation deals with how functions can best be approximated with simpler functions. In the study of approximation of functions by linear positive operators, Bernstein polynomials play a highly significant role due to their simple and useful structure. And, during the last few decades, different types of research have been dedicated to improving the rate of convergence and decreasing the error of approximation.
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Approximation theory.
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Summability theory.
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Approximation theory.
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Summability theory.
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Sequences, Series, Summability.
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Approximations and Expansions.
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Functional Analysis.
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| Dewey Classification
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515/.243
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| LC Classification
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QA295.A38 2018
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| Added Entry
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Acar, Tuncer
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Mohiuddine, S. A.
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