Certain exponential type $ m $-convexity inequalities for fractional integrals with exponential kernels
Open Access
- 1 January 2022
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 7 (4), 6311-6330
- https://doi.org/10.3934/math.2022351
Abstract
By applying exponential type $ m $-convexity, the Hölder inequality and the power mean inequality, this paper is devoted to conclude explicit bounds for the fractional integrals with exponential kernels inequalities, such as right-side Hadamard type, midpoint type, trapezoid type and Dragomir-Agarwal type inequalities. The results of this study are obtained for mappings $ \omega $ where $ \omega $ and $ |\omega'| $ (or $ |\omega'|^q $with $ q\geq 1 $) are exponential type $ m $-convex. Also, the results presented in this article provide generalizations of those given in earlier works.
Keywords
This publication has 27 references indexed in Scilit:
- Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach SpacesFractal and Fractional, 2019
- Hermite–Hadamard, Hermite–Hadamard–Fejér, Dragomir–Agarwal and Pachpatte type inequalities for convex functions via new fractional integralsJournal of Computational and Applied Mathematics, 2018
- Trapezoidal type inequalities related to h-convex functions with applicationsRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2018
- Montgomery identities and Ostrowski type inequalities for fractional integral operatorsRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2018
- On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operatorsFilomat, 2018
- k-fractional integral trapezium-like inequalities through ( h , m ) $(h,m)$ -convex and ( α , m ) $(\alpha,m)$ -convex mappingsJournal of Inequalities and Applications, 2017
- Ostrowski-type inequalities via h-convex functions with applications to special meansJournal of Inequalities and Applications, 2013
- Properties of -convex functions related to the Hermite–Hadamard–Fejér inequalitiesComputers & Mathematics with Applications, 2009
- On h-convexityJournal of Mathematical Analysis and Applications, 2007
- On some Hadamard-type inequalities for h-convex functionsJournal of Mathematical Inequalities, 2007