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Generalization of - Convex Stochastic Processes and Some Classical Inequalities

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  • Hao Zhou
  • Muhammad Shoaib Saleem
  • Mamoona Ghafoor
  • Jingjng Li

Abstract

The field of stochastic processes is essentially a branch of probability theory, treating probabilistic models that evolve in time. It is best viewed as a branch of mathematics, starting with the axioms of probability and containing a rich and fascinating set of results following from those axioms. In probability theory, a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function of the random variable. In this paper, the concept of generalized - convex stochastic processes is introduced, and some basic properties concerning generalized - convex stochastic processes are developed. Furthermore, we establish Jensen and Hermite–Hadamard and Fejér-type inequalities for this generalization.

Suggested Citation

  • Hao Zhou & Muhammad Shoaib Saleem & Mamoona Ghafoor & Jingjng Li, 2020. "Generalization of - Convex Stochastic Processes and Some Classical Inequalities," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, August.
    • Handle: RePEc:hin:jnlmpe:1583807
    DOI: 10.1155/2020/1583807
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