Abstract
In this note, our purpose is to introduce the concept of $ n $-polynomial convex stochastic processes and study some of their algebraic properties. We establish new refinements for integral version of Holder and power mean inequality. Also, we are concerned to extend several Hermite-Hadamard type inequalities for $ n $-polynomial convex stochastic processes by using Holder, Holder-Iscan, power mean and improved power mean integral inequalities. Moreover, we give comparison of obtained results.
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