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| FOUNDATIONS OF COMPLEX ANALYSIS IN NON LOCALLY CONVEX SPACES, 193
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Function Theory without Convexity Condition
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By
A. Bayoumi, King Saud University, College of Science, Mathematics Department, Riyadh 14511, Saudi Arabia
Included in series
North-Holland Mathematics Studies, 193
Description
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.
Audience
M.Sc. and Ph.D. students and reseachers in Analysis, especially in Complex and Functional Analysis.
Contents
1. Fundamental Theorems in F-Spaces.
2. Theory of Polynomials in F-Spaces.
3. Fixed-Point and P-Extreme Point.
4. Bayoumi
(Quasi) Differential Calculus.
5. Generalized Mean-Value Theorem.
6. Higher Quasi-Differential in F-Spaces.
7. Quasi-Holomorphic
Maps.
8. New Versions of Main Theorems.
9. Bounding and Weakly-Bounding Sets.
10. Levi Problem in Toplogical Spaces.
| Bibliographic details |
Hardbound, 304 pages, publication date: NOV-2003
ISBN-13: 978-0-444-50056-4
ISBN-10: 0-444-50056-1
Imprint: JAI
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| Price and Ordering |
Price:
USD 210
GBP 126.99
EUR 149.95
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Last update: 4 Sep 2009
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