A generalizations of Simpson's type inequality for differentiable functions using \(({\alpha},m)\)-convex functions and applications

DOI10.1186/1029-242X-2013-158zbMath1284.26035OpenAlexW2097442968WikidataQ59301693 ScholiaQ59301693MaRDI QIDQ394691

Shahid Qaisar, Chuanjiang He, Sabir Hussain

Publication date: 27 January 2014

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

Full work available at URL: https://doi.org/10.1186/1029-242x-2013-158

zbMATH Keywords

Hölder's inequalityspecial means\(({\alpha},m)\)-convex functionmid point inequalitySimpson's inequality

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (20)

Some Simpson type integral inequalities for functions whose third derivatives are (\(\alpha, m\))-GA-convex functions ⋮ New Simpson type integral inequalities for \(s\)-convex functions and their applications ⋮ PROPERTIES AND INTEGRAL INEQUALITIES INVOLVING WITH THE GENERALIZED s-TYPE PREINVEX MAPPINGS IN FRACTAL SPACE ⋮ On fractional Simpson type integral inequalities for co-ordinated convex functions ⋮ Some fractional Hermite-Hadamard-type integral inequalities with \(s\)-\((\alpha,m)\)-convex functions and their applications ⋮ New inequalities of Simpson's type for differentiable functions via generalized convex function ⋮ Some Simpson's Riemann-Liouville fractional integral inequalities with applications to special functions ⋮ Some new Hermite-Hadamard type inequalities for generalized harmonically convex functions involving local fractional integrals ⋮ SOME LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED PREINVEX FUNCTIONS AND APPLICATIONS TO NUMERICAL QUADRATURE ⋮ MORE RESULTS ON HERMITE-HADAMARD TYPE INEQUALITY THROUGH (<i>α, m</i>)-PREINVEXITY ⋮ Unnamed Item ⋮ Simpson-like type inequalities for relative semi-(α,m)-logarithmically convex functions ⋮ A generalization of Simpson's inequality via differentiable mapping using extended \((s,m)\)-convex functions ⋮ Generalized harmonically convex functions on fractal sets and related Hermite-Hadamard type inequalities ⋮ Certain new bounds considering the weighted Simpson-like type inequality and applications ⋮ More results on integral inequalities for strongly generalized \((\phi,h,s)\)-preinvex functions ⋮ Some results on integral inequalities via Riemann-Liouville fractional integrals ⋮ Simpson type integral inequalities for generalized fractional integral ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Some remarks on \(s\)-convex functions
• A theorem on mappings with bounded derivatives with applications to quadrature rules and means.
• Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula.
• On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula
• Inequalities for differentiable mappings with application to special means and quadrature formulæ
• An inequality of Simpson type

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