Abstract
The objective of this paper is to derive Hermite-Hadamard type inequalities for several higher order strongly h -preinvex functions via Riemann-Liouville fractional integrals. These results are the generalizations of the several known classes of preinvex functions. An identity associated with k-times differentiable function has been established involving Riemann-Liouville fractional integral operator. A number of new results can be deduced as consequences for the suitable choices of the parameters h and σ . Our outcomes with these new generalizations have the abilities to be implemented for the evaluation of many mathematical problems related to real world applications.
Highlights
The modeling of a few global problems requires using a fractional calculus which incorporates both derivatives and integrals
We presented the concept of higher order strongly h-preinvex functions with different kind of preinvexities
We establish an identity associated with differentiable functions of kth order using Riemann–Liouville fractional integral operator
Summary
The modeling of a few global problems requires using a fractional calculus which incorporates both derivatives and integrals. Sarikaya et al [22] employed the ideas of fractional calculus for establishing a number of integral inequalities that basically rely on Hermite–Hadamard inequality This approach has opened a new path for research. Xu [63] obtained new attributes of p-uniform convexity and q-uniform smoothness of a Banach space using k.k p and k.kq , respectively These outcomes can be acquired from the ideas of higher order strongly convex (concave) functions, which can be seen as a novel application. Noor et al [20] prolonged this idea utilizing the invexity property of sets and described the perception of h-preinvex functions They have perceived that it comprises of a few new and known classes of convexity. The principal intention of this research is to introduced the idea of higher order strongly h-preinvex functions. Utilizing this identity, we derive our main consequences for some upper bounds for kth order differentiable function via higher order strongly h-preinvex functions
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