Frontiers in Functional Equations and Analytic Inequalities
This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hypersta
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Frontiers in Functional Equations and Analytic Inequalities
Frontiers in Functional Equations and Analytic Inequalities
George A. Anastassiou • John Michael Rassias Editors
Frontiers in Functional Equations and Analytic Inequalities
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Editors George A. Anastassiou Department of Mathematical Sciences University of Memphis Memphis, TN, USA
John Michael Rassias National and Kapodistrian University of Athens Pedagogical Department E. E., Section of Mathematics and Informatics Athens, Greece
ISBN 978-3-030-28949-2 ISBN 978-3-030-28950-8 (eBook) https://doi.org/10.1007/978-3-030-28950-8 Mathematics Subject Classification: 26A33, 26D07, 26D10, 26D15, 26D20, 39Bxx, 30D05 © Springer Nature Switzerland AG 2019 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, expressed 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 Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To all the Great Mathematicians from Euclid (325 BC–265 BC) until Stanislaw Ulam (1909 AD–1984 AD)
Preface
This edited volume, Frontiers in Functional Equations and Analytic Inequalities, investigates functional equations and analytic inequalities in the broad sense and is written by authors who are in these mathematical fields for the past 50 years. It starts with fundamental notions of functional equations and analytic inequalities and several methods of solving functional equations and analytic inequalities in various spaces. It follows the progress of functional equations and analytic inequalities in the last five decades via excellent research chapters dedicated to the approximation and stability results of different types of functional equations and functional inequalities due to Abel, Cauchy, Euler, Lagrange, Jensen, Schröder, d’Alembert, Poisson, Drygas, Golab-Schinzel, etc., as well as very interesting new research result
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