Springer Optimization and Its Applications

Stability of Functional Equations in Random Normed Spaces

Authors: Cho, Yeol Je, Rassias, Themistocles M, Saadati, Reza

  • ​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​
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About this book

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.

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)


Table of contents (9 chapters)

  • Preliminaries

    Cho, Yeol Je (et al.)

    Pages 1-9

  • Generalized Spaces

    Cho, Yeol Je (et al.)

    Pages 11-45

  • Stability of Functional Equations in RN-Spaces Under Spacial t-Norm

    Cho, Yeol Je (et al.)

    Pages 47-61

  • Stability of Functional Equations in RN-Spaces Under Arbitrary t-Norms

    Cho, Yeol Je (et al.)

    Pages 63-80

  • Stability of Functional Equations in RN-Spaces via Fixed Point Methods

    Cho, Yeol Je (et al.)

    Pages 81-124

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-1-4614-8477-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-1-4614-8476-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Stability of Functional Equations in Random Normed Spaces
Authors
Series Title
Springer Optimization and Its Applications
Series Volume
86
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-8477-6
DOI
10.1007/978-1-4614-8477-6
Hardcover ISBN
978-1-4614-8476-9
Series ISSN
1931-6828
Edition Number
1
Number of Pages
XIX, 246
Topics