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- Foundations of Complex Analysis in Non Locally Convex Spaces
Foundations of Complex Analysis in Non Locally Convex Spaces
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The book contains new generalized versions of: 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, and, Fixed Point Theorems of Bruower, Schauder and Kakutani's. 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. The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in F-spaces without convexity conditions. 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. The book contains the theory of polynomials and Banach Stienhaus theorem in non convex spaces.
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