Stability of Functional Equations in Random Normed Spaces, 1st Edition

  • Published By:
  • ISBN-10: 1461484774
  • ISBN-13: 9781461484776
  • DDC: 515.75
  • Grade Level Range: College Freshman - College Senior
  • 246 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
1: Preliminaries.
2: Generalized Spaces.
3: Stability of Functional Equations in RN-Spaces Under Spacial t-Norm.
4: Stability of Functional Equations in RN-Spaces Under Arbitrary t-Norms.
5: Stability of Functional Equations in RN-Spaces via Fixed Point Methods.
6: Stability of Function Equations in Non-Archimedean Random Spaces.
7: Stability of Functional Equations Related to Inner Product Spaces.
8: Random Banach Algebras and Stability Results.
9: Related Results on Stability of Functional Inequalities and Equations.