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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. 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.
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. 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.
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.
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.
Some of the most recent and significant results on homomorphisms
and derivations in Banach algebras, quasi-Banach algebras,
C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras
and multi-normed algebras are presented in this book. A brief
introduction for functional equations and their stability is
provided with historical remarks. Since the homomorphisms and
derivations in Banach algebras are additive and R-linear or
C-linear, the stability problems for additive functional equations
and additive mappings are studied in detail. The latest results are
discussed and examined in stability theory for new functional
equations and functional inequalities in Banach algebras and
C*-algebras, non-Archimedean Banach algebras, non-Archimedean
C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate
students with an understanding of operator theory, functional
analysis, functional equations and analytic inequalities will find
this book useful for furthering their understanding and discovering
the latest results in mathematical analysis. Moreover, research
mathematicians, physicists and engineers will benefit from the
variety of old and new results, as well as theories and methods
presented in this book.
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.
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