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In this paper, several applications of the Hermite–Hadamard inequality for fractional integrals using G A -convexity are discussed, including some new refinements and similar extensions, as well as several applications in the Gamma and incomplete Gamma functions. [ABSTRACT FROM AUTHOR]

In this paper, new Fejér-type inequalities for harmonically convex functions are obtained. Some mappings related to the Fejér-type inequalities for harmonically convex are defined. Properties of these mappings are discussed and, as a consequence, we obtain refinements of some known results. [ABSTRACT FROM AUTHOR]

In this study, the Hermite–Hadamard–Fejér inequalities for G A -h-convex are proved, and the results for particular classes of functions are highlighted. In addition, several generalizations of the Hermite–Hadamard inequalities are presented. Some features of functions H and F that are naturally linked to the Hermite–Hadamard–Fejér-type inequalities for G A -h-convex have also been discussed. Finally, we obtain applications of the results related to the p-logarithmic mean and the mean of order p. [ABSTRACT FROM AUTHOR]

In this paper, some estimates of third and fourth inequalities in Hermite–Hadamard-type inequalities for coordinated convex functions are proved using the non-additivity of the integrals and Fubini's theorem for fuzzy integrals. That is, the results are obtained in the fuzzy context and using the Lebesgue measure. Several examples are provided on how to evaluate these estimates in order to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities. [ABSTRACT FROM AUTHOR]