Hermite–Hadamard Type Inequalities Involving k-Fractional Operator for (h¯,m)-Convex Functions
Soubhagya Kumar Sahoo, Hijaz Ahmad, Muhammad Tariq, Bibhakar Kodamasingh, Hassen Aydi, Manuel De la Sen
Abstract
The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q-polygamma special functions are presented.