Advances in Summability and Approximation Theory
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
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es in Summability and Approximation Theory
Advances in Summability and Approximation Theory
S. A. Mohiuddine Tuncer Acar •
Editors
Advances in Summability and Approximation Theory
123
Editors S. A. Mohiuddine Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science King Abdulaziz University Jeddah, Saudi Arabia
Tuncer Acar Department of Mathematics Selçuk University Selçuklu, Konya, Turkey
ISBN 978-981-13-3076-6 ISBN 978-981-13-3077-3 https://doi.org/10.1007/978-981-13-3077-3
(eBook)
Library of Congress Control Number: 2018960195 © Springer Nature Singapore Pte Ltd. 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
The aim of this book is to provide an up-to-date overview of the problems on summability and approximation theory, obtain some positive linear operators, and prove some approximation results. Of particular interest, the chapters in this book are devoted to the state-of-the-art research and development in summability and approximation theory. This book contains some original research papers by wellestablished mathematicians from the international mathematical community. This book will be of interest for a wide range of mathematicians whose area of research is summability and approximation theory. This book consists of 14 chapters. Chapter “Tauberian Conditions Under Which Convergence Follows from Statistical Summability by Weighted Means” is devoted to obtaining some Tauberian theorems for real and complex sequences involving the notion of statistical summability by weighted means. Chapter “Applications of Fixed Point Theorems and General Convergence in Orthogonal Metric Spaces” discusses the gene
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