AIMS Mathematics (Jun 2023)

Some well known inequalities for $ (h_1, h_2) $-convex stochastic process via interval set inclusion relation

  • Waqar Afzal,
  • Mujahid Abbas ,
  • Sayed M. Eldin,
  • Zareen A. Khan

DOI
https://doi.org/10.3934/math.20231015
Journal volume & issue
Vol. 8, no. 9
pp. 19913 – 19932

Abstract

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This note introduces the concept of $ (h_1, h_2) $-convex stochastic processes using interval-valued functions. First we develop Hermite-Hadmard $ (\mathbb{H.H}) $ type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for $ (h_1, h_2) $-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.

Keywords