Baron, Karol; Matkowski, Janusz; Nikodem, Kazimierz A sandwich with convexity. (English) Zbl 0803.39011 Math. Pannonica 5, No. 1, 139-144 (1994). It is the aim of this paper to characterize real functions which can be separated by a convex function. This leads the authors to the functional inequality \((*)\) \(f(tx + (1 - t)y) \leq tg(x) + (1 - t)g(y)\).The main result is given by Theorem 1: The real functions \(f\) and \(g\), defined on a real interval \(I\), satisfy \((*)\) for all \(x,y \in I\) and \(t \in [0,1]\) iff there exists a convex function \(h:I \to R\) such that \(f \leq h \leq g\).Using this sandwich theorem the authors characterize solutions of two functional inequalities connected with convex functions. They obtain also the classical one-dimensional Hyers-Ulam theorem on approximately convex functions. Reviewer: P.Talpalaru (Iaşi) Cited in 6 ReviewsCited in 27 Documents MSC: 39B72 Systems of functional equations and inequalities 26A51 Convexity of real functions in one variable, generalizations Keywords:real functions; convex function; functional inequality; sandwich theorem; Hyers-Ulam theorem PDFBibTeX XMLCite \textit{K. Baron} et al., Math. Pannonica 5, No. 1, 139--144 (1994; Zbl 0803.39011) Full Text: EuDML