Abstract
We introduce a new class of functions called strongly (eta,omega)-convex functions. This class of functions generalizes some recently introduced notions of convexity, namely, the η-convex functions and strongly η-convex functions. We also establish inequalities of the Hermite–Hadamard–Fejér’s type, which generalize results of Delavar and Dragomir (Math. Inequal. Appl. 20(1):203–216, 2017) and Awan et al. (Filomat 31(18):5783–5790, 2017). In addition, we obtain some new results for this class of functions. Finally, we apply our results to the k-Riemann–Liouville fractional integral operators to obtain more results in this direction.
Highlights
The field of mathematical inequalities, derived from different families of convexity, has been a booming area in recent times
2 A new class of convexity We introduce a new definition as a generalization of Definition 4
We present an example of a strongly (η, ω)-convex function
Summary
The field of mathematical inequalities, derived from different families of convexity, has been a booming area in recent times. The literature is replete with plethora of such results. The theory of inequalities, especially integral inequalities, has found its place in many areas of mathematical sciences. It is generally known that there are functions whose integrals cannot be computed analytically, but estimates of such integrals would suffice. An inequality is desired in this case. With the help of convexity the Jensen, Jensen–Steffensen, Slater, Favard, Berwald, Fejér, Hermite–Hadamard inequalities, and their generalizations have all been established. We concern ourselves with the Fejér and Hermite–Hadamard inequalities
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