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Advances in Summability and Approximation Theory

Editors: Mohiuddine, S. A., Acar, Tuncer (Eds.)

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  • Discusses the theory of classical and modern methods in summability
  • Includes a technique for studying the existence of solutions of infinite systems of differential equations in Banach sequence spaces
  • Introduces the approximation of functions by linear positive operators
  • Highlights interesting connections between convergence methods and approximation results
  • Presents original papers from active researchers around the globe
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eBook $84.99
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  • ISBN 978-981-13-3077-3
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Hardcover $109.99
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  • ISBN 978-981-13-3076-6
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  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

S. A. MOHIUDDINE is Full Professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. An active researcher, Professor Mohiuddine has coauthored one book, Convergence Methods for Double Sequences and Applications (Springer, 2014), and a number of book chapters, and has contributed over 120 research papers to various leading journals. He is a referee for several scientific journals and on the editorial board of numerous scientific journals, international scientific bodies and organizing committees. He has visited several international universities including Imperial College, London, UK. Professor Mohiuddine was a guest editor of a number of special issues for Abstract and Applied Analysis, Journal of Function Spaces and Scientific World Journal. His main research interests are in the field of functional analysis, sequence spaces, statistical convergence, matrix transformation, measures of noncompactness and approximation theory. 

TUNCER ACAR is Associate Professor at the Department of Mathematics, Faculty of Science, Selçuk University, Turkey. He previously worked at the Department of Mathematics and Statistics, the University of Alberta, Canada, as a visiting scholar in 2013 and 2014. He joined the Department of Mathematics, Faculty of Science, Kirikkale University, as a research assistant in 2009. He received his Master of Science degree in 2011, and Ph.D. degree in 2015, from the same university. Born in Amasya, Turkey, in 1985, Dr Acar is graduated from  Ataturk University, in 2008. He has studied approximation by linear positive operators and published about 40 papers.

Table of contents (14 chapters)

Table of contents (14 chapters)
  • Tauberian Conditions Under Which Convergence Follows from Statistical Summability by Weighted Means

    Önder, Zerrin (et al.)

    Pages 1-22

  • Applications of Fixed Point Theorems and General Convergence in Orthogonal Metric Spaces

    Hazarika, Bipan

    Pages 23-51

  • Application of Measure of Noncompactness to the Infinite Systems of Second-Order Differential Equations in Banach Sequence Spaces $$c,\ell _p$$ , and $$c_{0}^{\beta }$$

    Das, Anupam (et al.)

    Pages 53-70

  • Infinite Systems of Differential Equations in Banach Spaces Constructed by Fibonacci Numbers

    İlkhan, Merve (et al.)

    Pages 71-80

  • Convergence Properties of Genuine Bernstein–Durrmeyer Operators

    Acu, Ana-Maria

    Pages 81-101

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-981-13-3077-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-981-13-3076-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Advances in Summability and Approximation Theory
Editors
  • S. A. Mohiuddine
  • Tuncer Acar
Copyright
2018
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-3077-3
DOI
10.1007/978-981-13-3077-3
Hardcover ISBN
978-981-13-3076-6
Edition Number
1
Number of Pages
XIII, 241
Number of Illustrations
1 b/w illustrations, 9 illustrations in colour
Topics