Original scientific paper

Convexifiable functions in integral calculus

Sanjo Zlobec

Abstract

A function is said to be convexifiable if it becomes convex after adding to it a strictly convex quadratic term. In this paper we extend some of the basic integral properties of convex functions to Lipschitz continuously differentiable functions on real line. In particular, we give estimates of the mean value, a "nonstandard" form of Jensen's inequality, and an explicit representation of analytic functions. It is also outlined how one can use convexification to study ordinary differential equations.

Keywords

Convex function; convexifiable function; integral mean value; Jensen's inequality; analytic function

Hrčak ID:

377

URI

https://hrcak.srce.hr/377

Publication date:

9.11.2005.

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