Sitthiwirattham, ThaninAli, Muhammad AamirBudak, HuseyinChasreechai, Saowaluck2021-12-012021-12-0120212473-6988https://doi.org/10.3934/math.2021695https://hdl.handle.net/20.500.12684/10868In this paper, we introduce the notions of q-mean square integral for stochastic processes and co-ordinated stochastic processes. Furthermore, we establish some new quantum Hermite-Hadamard type inequalities for convex stochastic processes and co-ordinated stochastic processes via newly defined integrals. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as q, q(1), q(2) -> 1(-) in the newly obtained results.en10.3934/math.2021695info:eu-repo/semantics/openAccessHermite-Hadamard inequalityJensen inequalityconvex stochastic processesMidpoint-Type InequalitiesArticle61111989120102-s2.0-85113267949WOS:000697908400015Q2Q1