Hermite-Hadamard type mean square integral inequalities for stochastic processes whose twice mean square derivative are generalized η−convex

Abstract

In the present work, a new concept of generalized convexity (i.e. generalized η−convexity ) is established and applied to stochastic process.Using the aforementioned concept, some new Hermite - Hadamard type inequalities for stochastic processes are found. From these results, some other inequalities for convex stochastic processes and s-convex stochastic processes in the first sense are deduced. Some Lemmas are introduced and the classical H¨older and power mean inequalities are used as tools for the development of the main results.