Abstract
In this paper, we obtain a version of the Fejér–Hadamard inequality for harmonically convex functions via generalized fractional integral operator. In addition, we establish an integral identity and some Fejér–Hadamard type integral inequalities for harmonically convex functions via a generalized fractional integral operator. Being generalizations, our results reproduce some known results.
Highlights
Inequalities for convex functions, for example, the celebrated one is the Hermite–Hadamard inequality, providing a new horizon in the field of mathematical analysis
Many authors have been working on it continuously and several Hermite–Hadamard like integral inequalities have been established for many kinds of functions related to convex functions
The Hermite–Hadamard inequality for convex functions is stated in the following theorem
Summary
Inequalities for convex functions, for example, the celebrated one is the Hermite–Hadamard inequality, providing a new horizon in the field of mathematical analysis. The Hermite–Hadamard inequality for convex functions is stated in the following theorem. Let f : [ a, b] → R be a convex function and g : [ a, b] → R is non-negative, integrable and symmetric to a+2 b . We give the definition of harmonically convex functions.
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