# Foundations of Complex Analysis in Non Locally Convex Spaces, Vol 193. North-Holland Mathematics Studies

- ID: 1761778
- November 2003
- 304 Pages
- Elsevier Science and Technology

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,
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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.

Bayoumi, A.