| Summary: | In this thesis, we discuss about a point which minimize the value of a function
on normed space in analysis. At first, we introduce the convex sets and the convex
functions on normed space. The discussion in the convex set and the convex function
including the definition and basic properties of them. Furthermore, we discuss the
function that has lower semi-continuous from above, the Legendre-Fenchel transform
and subdifferentials of convex functions, and the constraint of extreme functions, and
we shall prove the Ekeland Variational Principle and the Borwein-Preiss Smooth
Variational Principle.
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