Some properties of <i>η</i>-convex stochastic processes

Chahn Yong Jung; Muhammad Shoaib Saleem; Shamas Bilal; Waqas Nazeer; Mamoona Ghafoor; Chahn Yong Jung; Muhammad Shoaib Saleem; Shamas Bilal; Waqas Nazeer; Mamoona Ghafoor

doi:10.3934/math.2021044

AIMS Mathematics

2021, Volume 6, Issue 1: 726-736. doi: 10.3934/math.2021044

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Research article

Some properties of η-convex stochastic processes

1.
Department of Business Administration, Gyeongsang National University, Jinju 52828, Korea
2.
Department of Mathematics, University of Okara, Okara-Pakistan
3.
Department of mathematics, university of Sialkot, Pakistan
4.
Department of Mathematics, GC University, Lahore-Pakistan

Received: 06 July 2020 Accepted: 15 October 2020 Published: 28 October 2020
MSC : Primary: 26A51; Secondary: 26A33, 33E12

The stochastic processes is a significant branch of probability theory, treating probabilistic models that develop in time. It is a part of mathematics, beginning with the axioms of probability and containing a rich and captivating arrangement of results following from those axioms. In probability, a convex function applied to the expected value of an random variable is always bounded above by the expected value of the convex function of the random variable. The definition of η-convex stochastic process is introduced in this paper. Moreover some basic properties of η-convex stochastic process are derived. We also derived Jensen, Hermite-Hadamard and Ostrowski type inequalities for η-convex stochastic process.
- stochastic process,
- η-convex function,
- η-convex stochastic processes,
- Hermite Hadmard type inequality,
- Ostrowski type inequality and Jensen inequality
Citation: Chahn Yong Jung, Muhammad Shoaib Saleem, Shamas Bilal, Waqas Nazeer, Mamoona Ghafoor. Some properties of η-convex stochastic processes[J]. AIMS Mathematics, 2021, 6(1): 726-736. doi: 10.3934/math.2021044

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Abstract

The stochastic processes is a significant branch of probability theory, treating probabilistic models that develop in time. It is a part of mathematics, beginning with the axioms of probability and containing a rich and captivating arrangement of results following from those axioms. In probability, a convex function applied to the expected value of an random variable is always bounded above by the expected value of the convex function of the random variable. The definition of η-convex stochastic process is introduced in this paper. Moreover some basic properties of η-convex stochastic process are derived. We also derived Jensen, Hermite-Hadamard and Ostrowski type inequalities for η-convex stochastic process.

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