A criterion forn-convexity
Peter S. Bullen · Pacific Journal of Mathematics · 1971
The development of the P n -integral of R. D. James and W. H. Gage is based on certain properties of π-convex functions.In order to develop this integral systematically a more detailed study of w-convex functions is needed.In the second section of this paper various derivatives are defined and some of their properties given; in the third and last sections properties of %-convex functions are developed.2* Definitions and some simple properties of generalized derivatives* Suppose F is a real-valued function defined on the bounded closed interval [α, b] then if it is true that for x 0 e ]a, b[ (1) *^±*>±*?*^ = ±β a "l-+ o(h») t asΛ-,0