Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness
This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept
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in Nonlinear Analysis via the Concept of Measure of Noncompactness
Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness
Józef Banaś Mohamed Jleli Mohammad Mursaleen Bessem Samet Calogero Vetro •
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Editors
Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness
123
Editors Józef Banaś Department of Nonlinear Analysis Rzeszów University of Technology Rzeszów Poland
Bessem Samet Department of Mathematics King Saud University Riyadh Saudi Arabia
Mohamed Jleli Department of Mathematics King Saud University Riyadh Saudi Arabia
Calogero Vetro Dipartimento di Matematica e Informatica University of Palermo Palermo Italy
Mohammad Mursaleen Department of Mathematics Aligarh Muslim University Aligarh, Uttar Pradesh India
ISBN 978-981-10-3721-4 DOI 10.1007/978-981-10-3722-1
ISBN 978-981-10-3722-1
(eBook)
Library of Congress Control Number: 2016963417 © Springer Nature Singapore Pte Ltd. 2017 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
The theory of measures of noncompactness constitutes a very important branch of nonlinear functional analysis. It finds a lot of applications in operator theory. First of all, it allows us to select very significant class of operators being generalizations of compact operators. Those operators are known as operators satisfying the Darbo condition or contractions with respect to a measure of noncompactness as well as condensing operators. Measures of noncompactness are widely applied in fixed point theory and are especially useful in investigations connected with the theories of differential equations, integral equations, functional inte
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