الفهرس 
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Abstract
This thesis consists of three chapters In chapter 1, we write the preliminaries, the fundamentalconcepts and theorems in functional analysis that we will
use through the thesis. Also we study the compactness of
linear operators.In chapter 2, we study Gâteaux differentiation and Fréchet
differentiation and their properties. Then Discuss and study Lipschitz functions, Lipschitz retraction, absolute Lipschitz retract and Lipschitz free Banach spaces. Finally we discuss some results on convex bodies.
In chapter 3, we study the modulus of continuity and its
properties then we discuss algebra of it. Also we study the
space of bounded real valued functions on normed spaces or
on metric spaces and its properties. Finally we get new
results.