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Convex function and its application in proving inequalities. (Chinese. English summary) Zbl 1107.26305

Summary: Convexity is an important geometry 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 functions. Especially, we study the applications of Jensen inequality of convex functions in proving inequalities.

MSC:

26D07 Inequalities involving other types of functions
52A40 Inequalities and extremum problems involving convexity in convex geometry
26A51 Convexity of real functions in one variable, generalizations
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