Quantum type integral inequalities for some convex stockastic processes

The aim of this study is to obtain quantum type integral inequalities, namely q-Hermite-Hadamard type, for some convex stochastic processes. In the introduction of this study, quantum calculus is briefly mentioned. In the second section, the basic concepts related to the subject of the study are presented. In the material and methods, mean-square convergence, continuity, differentiability and integrability are given for stochastic processes. In the research findings section, mean-square q-differential, q-derivative and q-integral operators are defined for stochastic processes and the properties of these operators are given. q-Hermite-Hadamard type integral inequalities are obtained for each of the convex, preinvex, φ-convex, harmonic convex, m-convex, r-convex, s-convex and (p,h)-convex stochastic processes separately.