Approximation of convex functions. (English) Zbl 1075.26003

Koliha, J. J.

Real Anal. Exch. 29(2003-2004), No. 1, 465-472 (2004).

It is known [M. Ghomi, Proc. Am. Math. Soc. 130, No. 8, 2255–2259 (2002; Zbl 0999.26008)] that every convex function on an open interval \(I\) can be uniformly approximated by convex \(C^\infty\)-functions on every compact subinterval \([a,b]\) of \(I\). Ghomi’s approach requires the knowledge of Lebesgue integral and convolutions. The aim of the paper under review is to give an elementary proof of the above mentioned approximation property requiring only first year calculus and linear algebra.

Reviewer: Wiesław Pleśniak (Kraków)

MSC:

26A51	Convexity of real functions in one variable, generalizations
41A30	Approximation by other special function classes
26E10	\(C^\infty\)-functions, quasi-analytic functions

Keywords:

convex function; convex \(C^\infty\)-function; approximation

Citations:

Zbl 0999.26008