Elementary Fixed Point Theorems
This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky’s theorem on periodic points, Thron’s results on the convergence of certain real
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P. V. Subrahmanyam
Elementary Fixed Point Theorems
Forum for Interdisciplinary Mathematics Editor-in-chief P. V. Subrahmanyam, Indian Institute of Technology Madras, Chennai, India Editorial Board Yogendra Prasad Chaubey, Concordia University, Montreal (Québec), Canada Jorge Cuellar, Principal Researcher, Siemens, Germany Janusz Matkowski, University of Zielona Góra, Poland Thiruvenkatachari Parthasarathy, Chennai Mathematical Institute, Kelambakkam, India Mathieu Dutour Sikirić, Rudjer Boúsković Institute, Zagreb, Croatia Bhu Dev Sharma, Jaypee Institute of Information Technology, Noida, India
The Forum for Interdisciplinary Mathematics series publishes high-quality monographs and lecture notes in mathematics and interdisciplinary areas where mathematics has a fundamental role, such as statistics, operations research, computer science, financial mathematics, industrial mathematics, and bio-mathematics. It reflects the increasing demand of researchers working at the interface between mathematics and other scientific disciplines.
More information about this series at http://www.springer.com/series/13386
P. V. Subrahmanyam
Elementary Fixed Point Theorems
123
P. V. Subrahmanyam (emeritus) Department of Mathematics Indian Institute of Technology Madras Chennai, Tamil Nadu, India
ISSN 2364-6748 ISSN 2364-6756 (electronic) Forum for Interdisciplinary Mathematics ISBN 978-981-13-3157-2 ISBN 978-981-13-3158-9 (eBook) https://doi.org/10.1007/978-981-13-3158-9 Library of Congress Control Number: 2018960278 © 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
Fixed point theorems constitute an important and interesting as
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