A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

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.

Hermite–Jensen–Mercer Type Inequalities for Caputo Fractional Derivatives

“…In recent years, inequality theory attracts many researchers due to its applications in our daily life and within the mathematics [1][2][3][4][5][6][7][8][9]. Let 0 < x 1 ≤ x 2 ≤ • • • ≤ x n and let μ � (μ 1 , μ 2 , .…”

Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions

“…ere are many well-known inequalities which have been extended for fractional calculus operators: for example, Hadamard, Minkowski, Ostrowski, Grüss, Ostrowski-Grüss, and Chebyshev inequalities have been extensively studied in recent decades, see [1][2][3][4][5][6][7][8]. e aim of this paper is to present the Hadamard and the Fejér-Hadamard inequalities for fractional integral operators for harmonically (α, h − m)-convex functions.…”

Inequalities for Riemann–Liouville Fractional Integrals of Strongly s , m -Convex Functions

“…e Hadamard inequality is one of the most studied inequalities for fractional integral operators. For some recent work, we refer the readers to [3,[8][9][10][11][12][13][14][15][16][17].…”