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

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...

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Published inAIMS mathematics Vol. 8; no. 9; pp. 19913 - 19932
Main Authors Afzal, Waqar, Abbas, Mujahid, Eldin, Sayed M., Khan, Zareen A.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
hermite-hadamard inequality
interval valued functions
jensen inequality
ostrowski inequality
stochastic process
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231015