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.
Highlights
The theory of convexity in mathematics has a rich history and has been a focus of intense investigation for more than a century
The Hermite–Hadamard inequality plays a crucial role in various fields of mathematics, especially in the theory of approximations
This paper aims to show that Hermite–Hadamard type inequalities are set up for consistently (h, m)-convex functions, which is concluded by using k-Riemann–Liouville fractional operators
Summary
The theory of convexity in mathematics has a rich history and has been a focus of intense investigation for more than a century. The celebrated Hermite–Hadamard inequality, coined separately by Charles Hermite and Jacques Hadamard, has attracted the interest of many mathematicians who have used various types of convex functions to yield many generalizations of the said inequality The Hermite–Hadamard inequality plays a crucial role in various fields of mathematics, especially in the theory of approximations Such inequalities have been studied extensively by many researchers, and a large number of generalizations and extensions of these for various kind of convex functions are established. This paper aims to show that Hermite–Hadamard type inequalities are set up for consistently (h, m)-convex functions, which is concluded by using k-Riemann–Liouville fractional operators. Employing this as an auxilliary result, we present some refinements of Hermite–Hadmard inequalities related to (h, m)-convex functions and some novel cases are elaborated.
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