Hermite-Hadamard-type inequalities for \(r\)-convex functions based on the use of Riemann-Liouville fractional integrals

DOI10.1007/s11253-013-0773-yzbMath1280.26044OpenAlexW2464211686MaRDI QIDQ384031

Mohammad Hasan, H. S. Yoon

Publication date: 25 November 2013

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-013-0773-y

zbMATH Keywords

differentiable \(r\)-convex functionsfractional integral identitiesHermite-Hadamard-type inequalities

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Inequalities for sums, series and integrals (26D15)

Related Items (20)

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Cites Work

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• Refinements of Hermite-Hadamard type inequalities involving fractional integrals
• On the generalization of some integral inequalities and their applications
• New inequalities of Ostrowski type for mappings whose derivatives are \(s\)-convex in the second sense via fractional integrals
• Hermite-Hadamard-type inequalities via \((\alpha ,m)\)-convexity
• Hermite-Hadamard's type inequalities for operator convex functions
• On weighted Hermite-Hadamard inequalities
• The Hermite-Hadamard inequality for log-convex functions
• Hermite-Hadamard's type inequalities for convex functions of selfadjoint operators in Hilbert spaces
• Hadamard-type and Bullen-type inequalities for Lipschitzian functions and their applications
• The Hermite-Hadamard inequality in Beckenbach's setting
• Fejer and Hermite-Hadamard type inequalities for superquadratic functions
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• On some inequalities of Hermite-Hadamard type via \(m\)-convexity
• A general multidimensional Hermite-Hadamard type inequality
• Hermite and convexity
• Convex functions, partial orderings, and statistical applications
• Stolarsky means and Hadamard's inequality
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities
• Exploring s-e-condition and applications to some Ostrowski type inequalities via Hadamard fractional integrals
• Hermite–Hadamard-type inequalities for Riemann–Liouville fractional integrals via two kinds of convexity
• r-convex functions

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