Some Inequalities for Multidimensional General h-Harmonic Preinvex and Strongly Generalized Convex Stochastic Processes
Shashi Kant Mishra, Nidhi Sharma, Jaya Bisht · 2023
In probability theory and other related fields, a stochastic process is a mathematical tool generally characterized as a group of random variables. Stochastic processes are broadly utilized as scientific models of systems that seem to shift in an arbitrary way. The notion of stochastic processes for convexity is of great importance in optimization and is also useful for numerical approximations when there exist probabilistic quantities. In this chapter, we introduce the concept of general h-harmonic preinvexity for real-valued stochastic processes and discuss some special cases of our definition. We prove Hermite-Hadamard-type inequalities for general h-harmonic preinvex stochastic processes. Further, we define multidimensional general h-harmonic preinvex stochastic processes and special cases in favour of the definition. Also, we obtain Hermite-Hadamard-type inequalities for multidimensional general h-harmonic preinvex stochastic processes. Furthermore, we introduce the concept of strongly η-convex stochastic processes. We prove the Hermite-Hadamard inequality, Ostrowski inequality and some other interesting inequalities for strongly η-convex stochastic processes.