Fractional generalized Hadamard and Fejér-Hadamard inequalities for <i>m</i>-convex functions
Xiuzhi Yang, Ghulam Farid, Waqas Nazeer, Yu‐Ming Chu, Chunfa Dong
Abstract
The objective of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities in generalized forms. By employing a generalized fractional integral operator containing extended generalized Mittag-Leffler function involving a monotone increasing function, we generalize the well known fractional Hadamard and Fejér-Hadamard inequalities for <i>m</i>-convex functions. Also we study the error bounds of these generalized inequalities. In connection with some published results from presented inequalities are obtained.
Topics & Concepts
Hadamard transformMathematicsHadamard three-lines theoremHadamard's inequalityConvex functionMittag-Leffler functionPure mathematicsFunction (biology)Monotone polygonConnection (principal bundle)Operator (biology)Fractional calculusRegular polygonHadamard productMathematical analysisCombinatoricsHadamard matrixGeometryBiochemistryEvolutionary biologyGeneChemistryRepressorTranscription factorBiologyMathematical Inequalities and ApplicationsFractional Differential Equations SolutionsNonlinear Differential Equations Analysis