Edition 
1st ed. 
Description 
1 online resource (xvi, 278 pages) : illustrations 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 
Series 
NorthHolland mathematics studies, 03040208 ; v. 193 

NorthHolland mathematics studies ; v. 193. 03040208

Summary 
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, nonconvex 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: HahnBanach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, pextreme points and applications in Operations Research, KreinMilman Theorem, Quasidifferential Calculus, Lagrange MeanValue Theorems, Taylor series, Quasiholomorphic and Quasianalytic maps, QuasiAnalytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, MeanValue Theorem for Definite Integral, Bounding and weaklybounding (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 Quasidifferentiability introduced by the author represents the backbone of the theory of Holomorphy for nonlocally convex spaces. In fact it is different but much stronger than the Frechet one. The book is intended not only for PostGraduate (M. Sc. & Ph. D.) students and researchers in Complex and Functional Analysis, but for all Scientists in various disciplines whom need nonlinear or nonconvex 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 MeanValue Theorem in real and complex cases, HahnBanach Theorems, Bolzano Theorem, KreinMilman 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 pExtreme points given by the author. bull; The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in Fspaces 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 Quasidifferential (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. 
Bibliography 
Includes bibliographical references (pages 262277) and index. 
Note 
Print version record. 
Contents 
Cover  Title Page  Copyright Page  Contents  CHAPTER 1. FUNDAMENTAL THEOREMS IN FSPACES  1.1 LINEAR MAPPINGS  1.2 HAHNBANACH THEOREMS  1.3 OPEN MAPPING THEOREM  1.4 UNIFORM BOUNDEDNESS PRINCIPLE  CHAPTER 2. THEORY OF POLYNOMIALS IN FSPACES  2.1 MULTILINEAR MAPS  2.2 POLYNOMIALS OF PNORMED SPACES  CHAPTER 3. FIXEDPOINT AND PEXTREME POINT  3.1 pEXTREME POINT IN NON LOCALLY CONVEX SPACES  3.2 GENERALIZED FIXED POINT THEOREM  3.3 GENERALIZED KREINMILMAN THEOREM  CHAPTER 4. QUASIDIFFERENTIAL CALCULUS  4.1 QUASIDIFFERENTIABLE MAPS  CHAPTER 5. GENERALIZED MEANVALUE THEOREM  5.1 MEANVALUE THEOREM IN REAL SPACES  5.2 MEANVALUE THEOREM IN COMPLEX SPACES  CHAPTER 6. HIGHER QUASIDIFFERENTIAL IN FSPACES  6.1 SCHWARTZ SYMMETRIC THEOREM  6.2 HIGHER QUASIDIFFERENTIALS  6.3 GENERAL SCHWARTZ SYMMETRIC THEOREM  6.4 DIRECTIONAL DERIVATIVES  6.5 QUASI AND FRIÉCHET DIFFERENTIALS  CHAPTER 7. QUASIHOLOMORPHIC MAPS  7.1 FINITE EXPANSIONS AND TAYLOR'S FORMULA  7.2 POWER SERIES IN FSPACES  7.3 QUASIANALYTIC MAPS  CHAPTER 8. NEW VERSIONS OF MAIN THEOREMS  8.1 FUNDAMENTAL THEOREM OF CALCULUS  8.2 BOLZANO'S INTERMEDIATE THEOREM  8.3 INTEGRAL MEANVALUE THEOREM  CHAPTER 9. BOUNDING AND WEAKLYBOUNDING SETS  9.1 BOUNDING SETS  9.2 WEAKLYBOUNDING (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(GRUMANKISELMAN APPROACH)  10.3 LEVI PROBLEM(SURJECTIVE LIMIT APPROACH)  10.4 LEVI PROBLEM(QUOTIENT MAP APPROACH)  Bibliography  Notations  Index  Last Page. 
Language 
English. 
Subject 
Holomorphic functions.


Functional analysis.


Convexity spaces.


Convex surfaces.


Complexes.


Fonctions holomorphes.


Analyse fonctionnelle.


Espaces de convexité.


Surfaces convexes.


Complexes (Mathématiques)


MATHEMATICS  Complex Analysis.


Complexes. (OCoLC)fst00871597


Convex surfaces. (OCoLC)fst00877265


Convexity spaces. (OCoLC)fst00877267


Functional analysis. (OCoLC)fst00936061


Holomorphic functions. (OCoLC)fst00958953

Genre/Form 
Electronic books.

Other Form: 
Print version: Bayoumi, Aboubakr. Foundations of complex analysis in non locally convex spaces. 1st ed. Amsterdam ; Boston : Elsevier, 2003 0444500561 9780444500564 (DLC) 2004272132 (OCoLC)53155238 
ISBN 
9780444500564 

0444500561 

008053192X (electronic bk.) 

9780080531922 (electronic bk.) 

1281029505 

9781281029508 

9786611029500 

6611029508 
Standard No. 
998077308 

AU@ 000048130722 

AU@ 000062577561 

CHNEW 001006531 

DEBBG BV036962309 

DEBBG BV039830177 

DEBBG BV042317319 

DEBSZ 27678250X 

DEBSZ 482354917 

NZ1 12433485 

NZ1 15192870 
