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2013 | Buch

Preliminaries Kapitel lesen Erstes Kapitel lesen

Stability of Functional Equations in Random Normed Spaces

verfasst von: Yeol Je Cho, Themistocles M. Rassias, Reza Saadati

Verlag: Springer New York

Buchreihe : Springer Optimization and Its Applications

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Preliminaries
Abstract
In this chapter, we recall some definitions and results which will be used later on in the book.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Chapter 2. Generalized Spaces
Abstract
In this chapter, we present some generalized spaces and their properties for the main results in this chapter.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Chapter 3. Stability of Functional Equations in RN-Spaces Under Spacial t-Norm
Abstract
In this chapter, we consider the stability of some functional equations in random normed spaces under the spacial t-norm, that is, T M via direct method.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Chapter 4. Stability of Functional Equations in RN-Spaces Under Arbitrary t-Norms
Abstract
In this chapter, we prove the stability of some functional equations in random, \(\mathcal{L}\)-random, intuitionistic random and fuzzy normed spaces under the arbitrary continuous t-norms.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Chapter 5. Stability of Functional Equations in RN-Spaces via Fixed Point Methods
Abstract
In this chapter, we consider some functional equations and prove their stability via fixed point methods in various random normed spaces.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Chapter 6. Stability of Function Equations in Non-Archimedean Random Spaces
Abstract
Throughout this chapter, we assume that X is a vector space and Y is a complete non-Archimedean normed space.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Chapter 7. Stability of Functional Equations Related to Inner Product Spaces
Abstract
In this chapter, we investigate the generalized Hyers–Ulam stability of functional equations in random normed spaces related to inner product spaces.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Chapter 8. Random Banach Algebras and Stability Results
Abstract
In this chapter, we define random normed algebras, provide some characteristic examples of them and also prove the stability of random homomorphisms, Cauchy–Jesen functional equations and random ∗-derivations in random Banach algebras.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Chapter 9. Related Results on Stability of Functional Inequalities and Equations
Abstract
In this chapter, we prove some stability results for certain functional inequalities and functional equations in latticetic random φ-normed spaces, r-divisible groups and homogeneous probabilistic (random) modular spaces.
Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Backmatter
Metadaten
Titel
Stability of Functional Equations in Random Normed Spaces
verfasst von
Yeol Je Cho
Themistocles M. Rassias
Reza Saadati
Copyright-Jahr
2013
Verlag
Springer New York
Electronic ISBN
978-1-4614-8477-6
Print ISBN
978-1-4614-8476-9
DOI
https://doi.org/10.1007/978-1-4614-8477-6