New multi-parametrized estimates having pth-order differentiability in fractional calculus for predominating h-convex functions in Hilbert space

In Hilbert space, we develop a novel framework to study for two new classes of convex function depending on arbitrary non-negative function, which is called a predominating h-convex function and predominating quasiconvex function, with respect to η, are presented. To ensure the symmetry of data segmentation and with the discussion of special cases, it is shown that these classes capture other classes of η-convex functions, η-quasiconvex functions, strongly h-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of κ-fractional integral operator to generate novel variants related to the Hermite-Hadamard type for pth-order differentiability. It is hoped that this research study will open new doors for in-depth investigation in convexity theory frameworks of a varying nature.