Jensen, Ostrowski and Hermite-Hadamard type inequalities for $ h $-convex stochastic processes by means of center-radius order relation

Abstract

In optimization, convex and non-convex functions play an important role. Further, there is no doubt that convexity and stochastic processes are closely related. In this study, we introduce the notion of the $ h- $convex stochastic process for center-radius order in the setting of interval-valued functions ($ \mathcal{IVFS} $) which is novel in literature. By using these notions we establish Jensen, Ostrowski, and Hermite-Hadamard ($ \mathcal{H.H} $) types inequalities for generalized interval-valued $ \mathcal{CR}-h $-convex stochastic processes. Furthermore, the study provides useful examples to support its findings.

Keywords

• hermite-hadamard
• ostrowski and jensen inequalities
• $ h $-convexity
• stochastic $ h $-convex