Trapezium-Type Inequalities for k -Fractional Integral via New Exponential-Type Convexity and Their Applications

In this paper, the authors investigated the concept of s,m-exponential-type convex functions and their algebraic properties. New generalizations of Hermite-Hadamard-type inequality for the s,m-exponential-type convex function ψ and for the products of two s,m-exponential-type convex functions ψ and φ are proved. Many refinements of the (H-H) inequality via s,m-exponential-type convex are obtained. Finally, several new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well. The ideas and techniques of this paper may stimulate further research in different areas of pure and applied sciences.