2005•Journal of Guangzhou UniversityRequires access

Convex function and its application in proving inequalities

Shujun You

Abstract

Convexity is an important geometric property. The convex function is a kind of function with special properties. Convexity and convex function have extensive applications in functional analysis, optimal theory, and mathematical economy. In this paper, we introduce the definition of convex function by the aid of convex set. We discuss some foundational properties of the convex function. Especially, we study the applications of Jensen inequality of convex function in proving inequalities.

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Key concepts: Convexity, Convex analysis, Subderivative, Pseudoconvex function, Proper convex function, Convex function, Convex set, Mathematics