All the existing books in Infinite Dimensional Complex Analysis
focus on the problems of locally convex spaces. However, the theory
without convexity condition is covered for the first time in this
book. This shows that we are really working with a new, important
and interesting field.
Theory of functions and nonlinear analysis problems are widespread
in the mathematical modeling of real world systems in a very broad
range of applications. During the past three decades many new
results from the author have helped to solve multiextreme problems
arising from important situations, non-convex and non linear cases,
in function theory.
Foundations of Complex Analysis in Non Locally Convex Spaces is a
comprehensive book that covers the fundamental theorems in Complex
and Functional Analysis and presents much new material.
The book includes generalized new forms of: Hahn-Banach Theorem,
Multilinear maps, theory of polynomials, Fixed Point Theorems,
p-extreme points and applications in Operations Research,
Krein-Milman Theorem, Quasi-differential Calculus, Lagrange
Mean-Value Theorems, Taylor series, Quasi-holomorphic and
Quasi-analytic maps, Quasi-Analytic continuations, Fundamental
Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for
Definite Integral, Bounding and weakly-bounding (limited) sets,
Holomorphic Completions, and Levi problem.
Each chapter contains illustrative examples to help the student and
researcher to enhance his knowledge of theory of functions.
The new concept of Quasi-differentiability introduced by the author
represents the backbone of the theory of Holomorphy for non-locally
convex spaces. In fact it is different but much stronger than the
Frechet one.
The book is intended not only for Post-Graduate (M.Sc.& Ph.D.)
students and researchers in Complex and Functional Analysis, but
for all Scientists in various disciplines whom need nonlinear or
non-convex analysis and holomorphy methods without convexity
conditions to model and solve problems.
bull; The book contains new generalized versions of:
i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in
real and complex cases, Hahn-Banach Theorems, Bolzano Theorem,
Krein-Milman Theorem, Mean value Theorem for Definite Integral, and
many others.
ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's.
bull; The book contains some applications in Operations research
and non convex analysis as a consequence of the new concept
p-Extreme points given by the author.
bull; The book contains a complete theory for Taylor Series
representations of the different types of holomorphic maps in
F-spaces without convexity conditions.
bull; The book contains a general new concept of differentiability
stronger than the Frechet one. This implies a new Differentiable
Calculus called Quasi-differential (or Bayoumi differential)
Calculus. It is due to the author's discovery in 1995.
bull; The book contains the theory of polynomials and Banach
Stienhaus theorem in non convex spaces.
General
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