Discrete Grüss type inequality on fractional calculus

DOI10.1186/s13660-015-0688-2zbMath1382.26017OpenAlexW1479847866WikidataQ59412415 ScholiaQ59412415MaRDI QIDQ264493

Serkan Aslıyüce, Ayşe Feza Güvenilir, Billur Kaymakçalan, Elvan Akın

Publication date: 31 March 2016

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

Full work available at URL: https://doi.org/10.1186/s13660-015-0688-2

zbMATH Keywords

discrete fractional calculusdiscrete Grüss inequality

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Inequalities for sums, series and integrals (26D15) Discrete version of topics in analysis (39A12) Other analytical inequalities (26D20)

Related Items (11)

Grüss type integral inequalities for generalized Riemann-Liouville \(k\)-fractional integrals ⋮ Some Grüss-type inequalities using generalized Katugampola fractional integral ⋮ More efficient estimates via \(\hslash\)-discrete fractional calculus theory and applications ⋮ Integral inequalities via Raina's fractional integrals operator with respect to a monotone function ⋮ Grüss-type integrals inequalities via generalized proportional fractional operators ⋮ Some \(k\)-fractional extension of Grüss-type inequalities via generalized Hilfer-Katugampola derivative ⋮ Chebyshev type inequality on nabla discrete fractional calculus ⋮ New formulation for discrete dynamical type inequalities via \(h\)-discrete fractional operator pertaining to nonsingular kernel ⋮ Grüss-type inequalities by means of generalized fractional integrals ⋮ Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions ⋮ New fractional order discrete Grüss type inequality

Cites Work

• Gronwall's inequality on discrete fractional calculus
• Continuity of solutions to discrete fractional initial value problems
• Modeling with fractional difference equations
• Nabla discrete fractional calculus and nabla inequalities
• The Grüss inequality on time scales
• A generalization of Grüss's inequality in inner product spaces and applications
• A Grüss type discrete inequality in inner product spaces and applications
• Grüss inequality for completely bounded maps
• Nabla discrete fractional Grüss type inequality
• Multivariate Fink type identity and multivariate Ostrowski, comparison of means and Grüss type inequalities
• Notes on a Grüss type inequatility and its application
• Initial value problems in discrete fractional calculus
• On a New Definition of the Fractional Difference
• Differences of Fractional Order
• A discrete fractional Gronwall inequality
• Analytic Inequalities
• Über das Maximum des absoluten Betrages von \[ \frac 1{b-a}\int _a^bf(x)g(x)\,dx-\frac 1{(b-a)^2}\int _a^bf(x)\,dx\int _a^bg(x)\,dx. \ .]
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Discrete Grüss type inequality on fractional calculus