Glasnik matematički, Vol. 40 No. 2, 2005.
Izvorni znanstveni članak
Convexifiable functions in integral calculus
Sanjo Zlobec
Sažetak
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.
Ključne riječi
Convex function; convexifiable function; integral mean value; Jensen's inequality; analytic function
Hrčak ID:
377
URI
Datum izdavanja:
9.11.2005.
Posjeta: 1.343 *