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Foundations of complex analysis in non locally convex spaces function theory without convexity condition

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

Bibliographic Details
Main Author: Bayoumi, Aboubakr
Format: eBook
Language:English
Published: Amsterdam Elsevier 2003, 2003
Edition:1st ed
Series:North-Holland mathematics studies
Subjects:
Convex Surfaces / Http://id.loc.gov/authorities/subjects/sh85031732
Surfaces Convexes
Holomorphic Functions / Http://id.loc.gov/authorities/subjects/sh85061536
Convex Surfaces / Fast / (ocolc)fst00877265
Complexes / Fast / (ocolc)fst00871597
Mathematics / Complex Analysis / Bisacsh
Complexes / Http://id.loc.gov/authorities/subjects/sh85029372
Functional Analysis / Fast / (ocolc)fst00936061
Functional Analysis / Http://id.loc.gov/authorities/subjects/sh85052312
Convexity Spaces / Fast / (ocolc)fst00877267
Convexity Spaces / Http://id.loc.gov/authorities/subjects/sh85031733
Fonctions Holomorphes
Complexes (mathématiques)
Espaces De Convexité
Analyse Fonctionnelle
Holomorphic Functions / Fast / (ocolc)fst00958953
Online Access:
Collection: Elsevier eBook collection Mathematics - Collection details see MPG.ReNa
Table of Contents:
  • Cover
  • Title Page
  • Copyright Page
  • 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 FRIÉCHET 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(SURJECTIVE LIMIT APPROACH)
  • 10.4 LEVI PROBLEM(QUOTIENT MAP APPROACH)
  • Bibliography
  • Notations
  • Index
  • Last Page
  • Includes bibliographical references (pages 262-277) and index

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