New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals

Abstract

In this paper, we present an identity for differentiable functions that has played an important role in proving Hermite–Hadamard type inequalities for functions whose absolute values of first derivatives are <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>s</a:mi></a:math> -convex functions. Meanwhile, some Hermite–Hadamard type inequalities for the functions whose absolute values of second derivatives are <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mi>s</c:mi></c:math> -convex are also established with the help of an existing identity in literature. Many limiting results are deduced from the main results which are stated in remarks. Some applications of proved results are also discussed in the present study.