Dedicated to Professor János Aczél on the occasion of his 80 th birthday Summary. Applying some fundamental results concerning moment spaces induced by Tchebychev systems, we establish Hermite-Hadamard type inequalities for generalized convex functions. (2000). Primary 26A51, 26B25, 26D15.
Mathematics Subject Classification
Abstract. In this paper we investigate (ω 1 , ω 2 ) -convex functions and obtain characterization theorems and Hadamard-type inequalities for them. (2000): 26A51, 26B25.
Mathematics subject classification
The Hermite-Hadamard inequality not only is a consequence of convexity but also characterizes it: if a continuous function satisfies either its left-hand side or its right-hand side on each compact subinterval of the domain, then it is necessarily convex. The aim of this paper is to prove analogous statements for the higher-order extensions of the Hermite-Hadamard inequality. The main tools of the proofs are smoothing by convolution and the support properties of higher-order monotone functions.
Abstract. The classical Hermite-Hadamard inequality, under some weak regularity conditions, characterizes convexity. The aim of the present paper is to give analogous result for the case of generalized convexity induced by two dimensional Chebyshev systems. The basic tool of the proofs is a characterization theorem of continuous, non-convex functions.Mathematics subject classification (2000): 26A51, 26B25, 26D15.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.