Fixed Point Theory in Metric Type Spaces
Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed poin
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d Point Theory in Metric Type Spaces
Fixed Point Theory in Metric Type Spaces
Ravi P. Agarwal • Erdal Karapınar • Donal O’Regan Antonio Francisco Roldán-López-de-Hierro
Fixed Point Theory in Metric Type Spaces
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Ravi P. Agarwal Department of Mathematics Texas A&M University-Kingsville Kingsville, Texas, USA
Erdal Karapınar Department of Mathematics Atılım University Incek, Ankara, Turkey
Donal O’Regan National University of Ireland Galway, Galway, Ireland
Antonio Francisco Roldán-López-de-Hierro Department of Quantitative Methods for Economics and Business University of Granada Granada, Spain
ISBN 978-3-319-24080-0 ISBN 978-3-319-24082-4 (eBook) DOI 10.1007/978-3-319-24082-4 Library of Congress Control Number: 2015953665 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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 Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)
Ravi P. Agarwal: To my wife Sadhna. Erdal Karapınar: To my wife Senem Pınar and our child Ula¸s Ege. Donal O’Regan: To my wife Alice and our children Aoife, Lorna, Daniel, and Niamh. Antonio F. Roldán-López-de-Hierro: To my wife María José, our daughters Ana and Sofía, and my parents María Dolores and Antonio.
Preface
Fixed-point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real-world problems, fixed-point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed-point theory is an important area of study in pure and applied mathematics, and it is a flourishing area of research. As the title states, this is a book on metric fixed-point theory where the basic ideas come from metric space topology. We present a self-contained account of the theory (techniques and results) in metric-type spaces (in part
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