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© 2013

Stability of Functional Equations in Random Normed Spaces

Benefits

  • Presents results proved in detail with several outlines examples to make the presentation of the theory well understood by large audiences

  • Discusses useful research to both pure and applied mathematicians who search for both new and old results

  • Presents written results for scientists and engineers who are orienting their study in the language of interdisciplinary research?

Book

Part of the Springer Optimization and Its Applications book series (SOIA, volume 86)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 1-9
  3. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 11-45
  4. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 47-61
  5. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 63-80
  6. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 81-124
  7. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 125-151
  8. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 153-173
  9. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 175-205
  10. Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
    Pages 207-233
  11. Back Matter
    Pages 235-246

About this book

Introduction

This book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject  was proposed by Stan M. Ulam in 1940 for approximate homomorphisms. The seminal work of Donald H. Hyers in 1941 and that of Themistocles M. Rassias in 1978 have provided a great deal of inspiration and guidance for mathematicians worldwide  to investigate this extensive domain of research.

The book presents a self-contained survey of recent and new results on topics including basic theory of random normed spaces and related spaces; stability theory for new function equations in random normed spaces via fixed point method, under both special and arbitrary t-norms; stability theory of well-known new functional equations in non-Archimedean random normed spaces; and applications in the class of fuzzy normed spaces. It contains valuable results on stability in random normed spaces, and is geared toward both graduate students and research mathematicians and engineers in a broad area of interdisciplinary research.

Keywords

functional equations in generalized spaces non-Archimedean random spaces random normed spaces via fixed point method stability of functional equations t-norms

Authors and affiliations

  1. 1.Gyeongsang National UniversityChinjuKorea, Republic of (South Korea)
  2. 2.National Technical University of AthensAthensGreece
  3. 3.Iran University of Science and TechnologyBehshahrIran

Bibliographic information

  • Book Title Stability of Functional Equations in Random Normed Spaces
  • Authors Yeol Je Cho
    Themistocles M. Rassias
    Reza Saadati
  • Series Title Springer Optimization and Its Applications
  • Series Abbreviated Title Springer Optimization
  • DOI https://doi.org/10.1007/978-1-4614-8477-6
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4614-8476-9
  • Softcover ISBN 978-1-4939-0110-4
  • eBook ISBN 978-1-4614-8477-6
  • Series ISSN 1931-6828
  • Edition Number 1
  • Number of Pages XIX, 246
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Functional Analysis
    Optimization
    Partial Differential Equations
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

“The book should interest any professional mathematician whose research is connected with functional equations, especially their stability in random spaces; I also can recommend it for graduate students interested in the subject. It could serve as a complete and independent introduction to the field of stability of functional equations in random spaces and as an excellent source of references for further study.” (Janusz Brzdęk, SIAM Review, Vol. 57 (1), March, 2015)

“The book under review is essentially a collection of several recent papers related to the stability of functional equations in the framework of fuzzy and random normed spaces. … useful for graduate students who are interested in the Hyers-Ulam-Rassias stability of functional equations.” (Mohammad Sal Moslehian, zbMATH, Vol. 1281, 2014)