Foundations of Complex Analysis in Non Locally Convex Spaces Function Theory Without Convexity Condition 1st Edition by Aboubakr Bayoumi ISBN 008053192 9780444500564X

Foundations of Complex Analysis in Non Locally Convex Spaces Function Theory Without Convexity Condition 1st Edition by Aboubakr Bayoumi – Ebook PDF Instant Download/Delivery: 008053192, 9780444500564X
Full download Foundations of Complex Analysis in Non Locally Convex Spaces Function Theory Without Convexity Condition 1st Edition after payment

Product details:

ISBN 10: 008053192 
ISBN 13: 9780444500564X
Author: Aboubakr Bayoumi

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.

Foundations of Complex Analysis in Non Locally Convex Spaces Function Theory Without Convexity Condition 1st Table of contents:

Chapter 1: Fundamental Theorems in F-Spaces
1.1 LINEAR MAPPINGS
1.2 HAHN-BANACH THEOREMS
1.3 OPEN MAPPING THEOREM
1.4 UNIFORM BOUNDEDNESS PRINCIPLE
Chapter 2: Theory of Polynomials in F-Spaces
2.1 MULTILINEAR MAPS
2.2 POLYNOMIALS OF P-NORMED SPACES
Chapter 3: Fixed-Point and P-Extreme Point
3.1 p-EXTREME POINT IN NON LOCALLY CONVEX SPACES
3.2 GENERALIZED FIXED POINT THEOREM
3.3 GENERALIZED KREIN-MILMAN THEOREM
Chapter 4: Quasi-Differential Calculus
4.1 QUASI-DIFFERENTIABLE MAPS
Chapter 5: Generalized Mean-Value Theorem
5.1 MEAN-VALUE THEOREM IN REAL SPACES
5.2 MEAN-VALUE THEOREM IN COMPLEX SPACES
Chapter 6: Higher Quasi-Differential in F-Spaces
6.1 SCHWARTZ SYMMETRIC THEOREM
6.2 HIGHER QUASI-DIFFERENTIALS
6.3 GENERAL SCHWARTZ SYMMETRIC THEOREM
6.4 DIRECTIONAL DERIVATIVES
6.5 QUASI AND FRÉCHET DIFFERENTIALS
Chapter 7: Quasi-Holomorphic Maps
7.1 FINITE EXPANSIONS AND TAYLOR’s FORMULA
7.2 POWER SERIES IN F-SPACES
7.3 QUASI-ANALYTIC MAPS
Chapter 8: New Versions of Main Theorems
8.1 FUNDAMENTAL THEOREM OF CALCULUS
8.2 BOLZANO’S INTERMEDIATE THEOREM
8.3 INTEGRAL MEAN-VALUE THEOREM
Chapter 9: Bounding and Weakly-Bounding SetS
9.1 BOUNDING SETS
9.2 WEAKLY-BOUNDING (LIMITED) SETS
9.3 PROPERTIES OF BOUNDING AND LIMITED SETS
9.4 HOLOMORPHIC COMPLETION
Chapter 10: Levi Problem in Toplogical Spaces
10.1 LEVI PROBLEM AND RADIUS OF CONVERGENCE
10.2 LEVI PROBLEM (GRUMAN-KISELMAN APPROACH)
10.3 LEVI PROBLEM (SUBJECTIVE LIMIT APPROACH)
10.4 LEVI PROBLEM (QUOTIENT MAP APPROACH)

People also search for Foundations of Complex Analysis in Non Locally Convex Spaces Function Theory Without Convexity Condition 1st:

s ponnusamy foundations of complex analysis pdf
    
s ponnusamy foundations of complex analysis
    
borrow foundations of complex analysis
    
synopsis of foundations of complex analysis
    
foundations of complex analysis ponnusamy pdf free download

Tags:

Aboubakr Bayoumi,Complex Analysis,Convex Spaces,Convexity