Hermite-Hadamard Type Inequalities for <i>s</i>-Convex Stochastic Processes in the Second Sense

Abstract

In this study, s-convex stochastic processes in the second sense are presented and some well-known results concerning s-convex functions are extended to s-convex stochastic processes in the second sense. Also, we investigate relation between s-convex stochastic processes in the second sense and convex stochastic processes.

Generalized Fractional Inequalities of the Hermite–Hadamard Type for Convex Stochastic Processes

“…Loads of estimates can be deduced as special cases of our main theorems. For related results, we invite the interested reader to the following papers [4,9,10,11,12,13] and the references cited therein.…”

Some integral inequalities of the Hermite-Hadamard type for s-convex stochastic processes on n-coordinates

“…for each i 2 1; 2;âej; n 1. Using the inequalities (10) and (11) in (9) and taking summation from 1 to n 1, we have (8).…”

“…Shortly, let us mention two types of s-convex stochastic processes in [10]- [11]. Let …x s 2 (0; 1] and the stochastic process X : [0; 1) !…”

A New Hermite-Hadamard inequality for h-convex stochastic processes

“…Obviously, if we take h(λ ) = λ and h(λ ) = λ s in (5), then the definition of h−convex stochastic process reduces to the definition of classical convex stochastic process [10] and s−convex stochastic process in the second sense [12] respectively. Moreover, A stochastic process X : I × Ω → R is:…”