Hermite-Hadamard type inequalities for p-convex stochastic processes

Abstract

In this study are investigated p-convex stochastic processes which are extensionsof convex stochastic processes. A suitable example is also given for this process.In addition, in this case a p-convex stochastic process is increasing or decreasing,the relation with convexity is revealed. The concept of inequality as convexityhas an important place in literature, since it provides a broader setting to studythe optimization and mathematical programming problems. Therefore, Hermite-Hadamard type inequalities for p-convex stochastic processes and someboundaries for these inequalities are obtained in present study. It is used theconcept of mean-square integrability for stochastic processes to obtain the abovementioned results.