Hermite-Hadamard-type inequalities for functions whose derivatives are \(\eta\)-convex via fractional integrals

DOI10.1186/S13660-019-1993-YzbMath1499.26138OpenAlexW2806100907MaRDI QIDQ2067759

Young-Chel Kwun, Waqas Nazeer, Mamoona Ghafoor, Muhammad Shoaib Saleem, Kang, Shin Min

Publication date: 19 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-019-1993-y

zbMATH Keywords

convex functionfractional integralHermite-Hadamard-type inequality\( \eta\)-convex function

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51) Means (26E60) Inequalities involving derivatives and differential and integral operators (26D10) Inequalities involving other types of functions (26D07)

Related Items (12)

Numerical approximation of Riccati fractional differential equation in the sense of Caputo-type fractional derivative ⋮ Strongly reciprocally \(p\)-convex functions and some inequalities ⋮ On generalized strongly \(p\)-convex functions of higher order ⋮ Hermite-Jensen-Mercer type inequalities for Caputo fractional derivatives ⋮ New Hermite-Hadamard type inequalities for \(\psi \)-Riemann-Liouville fractional integral via convex functions ⋮ Operator \((p,\eta)\)-convexity and some classical inequalities ⋮ Fractional integral inequalities of Hermite-Hadamard type for differentiable generalized \(h\)-convex functions ⋮ On Caputo-Fabrizio fractional integral inequalities of Hermite-Hadamard type for modified \(h\)-convex functions ⋮ New Trapezoid Type Inequalities for Generalized Exponentially Strongly Convex Functions ⋮ On strongly convex functions via Caputo-Fabrizio-type fractional integral and some applications ⋮ Inequalities for unified integral operators via strongly \((\alpha ,h\text{-}m)\)-convexity ⋮ Hermite-Hadamard- and Jensen-type inequalities for interval \((h_1,h_2)\) nonconvex function

Cites Work

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• Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means
• Hadamard-type inequalities for s-convex functions
• On some inequalities for s-convex functions and applications
• On φ-convex functions
• Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals
• On some Hadamard-type inequalities for h-convex functions
• THE HADAMARD INEQUALITIES FOR s-CONVEX FUNCTIONS IN THE SECOND SENSE

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