Abstract
The stochastic process is one of the important branches of probability theory which deals with probabilistic models that evolve over time. It starts with probability postulates and includes a captivating arrangement of conclusions from those postulates. In probability theory, a convex function applied on the expected value of a random variable is always bounded above by the expected value of the convex function of that random variable. The purpose of this note is to introduce the class of generalized p -convex stochastic processes. Some well-known results of generalized p -convex functions such as Hermite-Hadamard, Jensen, and fractional integral inequalities are extended for generalized p -stochastic convexity.
Highlights
A stochastic process is a mathematical tool commonly defined as a set of random variables in various fields of probability
Random variables were related to or listed by a lot of numbers, normally as focuses in time, giving the translation of a stochastic process, speaking to numerical estimations, some systems randomly changing over time, such as the growth of bacterial populations, fluctuations in electrical flow due to thermal noise, or the production of gas molecules
Stochastic systems are commonly used as scientific models of systems that tend to alter in an arbitrary manner. ey have applications in various fields, especially in sciences, for instance, chemistry, physics, biology, neuroscience, and ecology, in addition to technology and engineering fields, for example, picture preparing, cryptography, signal processing, telecommunications, PC science, and data theory
Summary
A stochastic process is a mathematical tool commonly defined as a set of random variables in various fields of probability. Erefore, Schur type, Hermite-Hadamard, Jensen, and fractional integral inequalities and some important results for the above said processes will be obtained in this study. Let us consider the Jensen-convex stochastic process ξ: I × Ω ⟶ R that is mean-square continuous on I; we have ξa1 + a2 , . ≤. Let us present some important generalizations of convex Definition 11. Consider a stochastic process ξ: (0, ∞) × Ω ⟶ R defined by ξ(u, .) up, p ≠ 0, and η(x, y) x − y; ξ is the generalized p-convex. E third, fourth, and fifth sections are devoted to Hermite-Hadamard, Jensen, and fractional integral inequalities for generalized p-convex stochastic processes.
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