On convex functions of higher order

Abstract

Abstract. Based on J. L. W. V. Jensen's concept of convex functions as well on its generalization by E. M. Wright and related to T. Popoviciu's convexity notions, higher-order convexity properties of real functions are introduced and surveyed.Mathematics subject classification (2000): 26A51, 26A48, 39B62.

Approximate convexity of Takagi type functions

“…Wright [37], Gilányi and Páles [6,7]). In the case of continuity, the Wrightconvexity is equivalent to convexity of φ.…”

Decomposition of higher-order Wright-convex functions

“…It seems to be natural to introduce the notion of the Wright-convexity of order n, as well. In the paper [4] the following definition has been given: For n ∈ N, a function f : I → R is called Wright-convex of order n (or shortly n- Wright-…”

On Some Recent Applications of Stochastic Convex Ordering Theorems to Some Functional Inequalities for Convex Functions: A Survey

“…In [41], Lemma 2 is used to prove results, which extend the inequalities (18) and (20) and inequalities between quadrature operators.…”