Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications.
<ul>
<li>Explores random differentiation and random integral equations</li>
<li>Delves into the study of random operator theory</li>
<li>Discusses the concept of random Banach algebras and its applications</li>
</ul>

Random Operator Theory

Science & Math

Saadati, Reza

Mathematics

Academic Press

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.

Stability of Functional Equations in Random Normed Spaces (Springer Optimization and Its Applications, 86)

Rassias, Themistocles M.

Cho, Yeol Je

Springer

Cho, Yeol Je Je

This self-contained monograph presents an overview of fuzzy operator theory in mathematical analysis. Concepts, principles, methods, techniques, and applications of fuzzy operator theory are unified in this book to provide an introduction to graduate students and researchers in mathematics, applied sciences, physics, engineering, optimization, and operations research.  New approaches to fuzzy operator theory and fixed point theory with applications to fuzzy metric spaces, fuzzy normed spaces, partially ordered fuzzy metric spaces, fuzzy normed algebras, and non-Archimedean fuzzy metric spaces are presented. Surveys are provided on: Basic theory of fuzzy metric and normed spaces and its topology, fuzzy normed and Banach spaces, linear operators, fundamental theorems (open mapping and closed graph), applications of contractions and fixed point theory, approximation theory and best proximity theory, fuzzy metric type space, topology and applications.

Fuzzy Operator Theory in Mathematical Analysis

This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. &nbsp;Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.

Advances in Matrix Inequalities (Springer Optimization and Its Applications, 176)

Ghaemi, Mohammad Bagher

Gharakhanlu, Nahid

Advances in Matrix Inequalities (Springer Optimization and Its Applications)

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