NEW INEQUALITIES OF HERMITE-HADAMARD TYPE FOR n-POLYNOMIAL s-TYPE CONVEX STOCHASTIC PROCESSES

The purpose of this paper is to introduce a more generalized class of convex stochastic processes and explore some of their algebraic properties. This new class of stochastic processes is called the n-polynomial s-type convex stochastic process. We demonstrate that this new class of stochastic processes leads to the discovery of novel Hermite-Hadamard type inequalities. These inequalities provide upper bounds on the integral of a convex function over an interval in terms of the moments of the stochastic process and the convexity parameter s. To compare the effectiveness of the newly discovered Hermite-Hadamard type inequalities, we also consider other commonly used integral inequalities, such as Holder, Holder-iscan, and power-mean, as well as improved power-mean integral inequalities. We show that the Holder-iscan and improved power-mean integral inequalities provide a better approach for the n-polynomial s-type convex stochastic process than the other integral inequalities. Finally, we provide some applications of the Hermite-Hadamard type inequalities to special means of real numbers. Our findings provide a useful tool for the analysis of stochastic processes in various fields, including finance, economics, and engineering.