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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 Holder and power mean inequalities are used as tools for the development of the main results.