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Contains both classical and modern methods in summability theory Focuses on the basic developments concerning an idea in full details Integrates theories as well as applications, wherever possible This book discusses recent developments in and contemporary research on summability theory, including general summability methods, direct theorems on summability, absolute and strong summability, special methods of summability, functional analytic methods in summability, and related topics and applications. All contributing authors are eminent scientists, researchers and scholars in their respective fields, and hail from around the world. Summability theory is generally used in analysis and applied mathematics. It plays an important part in the engineering sciences, and various aspects of the theory have long since been studied by researchers all over the world. Audience The book can be used as a textbook for graduate and senior undergraduate students, and as a valuable reference guide for researchers and practitioners in the fields of summability theory and functional analysis. Topics Sequences, Series, Summability Functional Analysis Approximations and Expansions
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Hemen Dutta · Billy E. Rhoades Editors Current Topics in Summability Theory and Applications Current Topics in Summability Theory and Applications Hemen Dutta Billy E. Rhoades • Editors Current Topics in Summability Theory and Applications 123 Editors Hemen Dutta Department of Mathematics Gauhati University Guwahati, Assam India ISBN 978-981-10-0912-9 DOI 10.1007/978-981-10-0913-6 Billy E. Rhoades Department of Mathematics Indiana University Bloomington, IN USA ISBN 978-981-10-0913-6 (eBook) Library of Congress Control Number: 2016931604 © Springer Science+Business Media Singapore 2016 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd. Preface This book is intended for graduate students and researchers who have interest in functional analysis, in general and summability theory, in particular. It describes several useful topics in summability theory along with applications. The book consists of nine chapters and is organized as follows: Chapter “An Introduction to Summability Methods” is introductory in nature. This chapter focuses on the historical development of summability theory right from Cauchy’s concept to till date. Summability methods developed from the two basic processes—T-process and /-process—have also been discussed in this chapter. Chapter “Some Topics in Summability