Dergiler / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 2

IMPROVED HERMITE HADAMARD TYPE INEQUALITIES FOR HARMONICALLY CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS

IMPROVED HERMITE HADAMARD TYPE INEQUALITIES FOR HARMONICALLY CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS

Zeynep ŞANLI, Tuncay KÖROĞLU, Mehmet KUNT

Sayfa
1556–1575
DOI
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Abstract

In this paper, we prove three new Katugampola fractional HermiteHadamard type inequalities for harmonically convex functions by using the leftand the right fractional integrals independently. One of our Katugampola fractional Hermite-Hadamard type inequalities is better than given in [17]. Also,we give two new Katugampola fractional identities for di§erentiable functions.By using these identities, we obtain some new trapezoidal type inequalitiesfor harmonically convex functions. Our results generalize many results fromearlier papers.