Grüss-type and Ostrowski-type inequalities in approximation theory

DOI10.1007/s11253-011-0548-2zbMath1254.41011OpenAlexW2021065822MaRDI QIDQ1759949

Ioan Raşa, Heinz H. Gonska, Ana-Maria Acu

Publication date: 23 November 2012

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

Full work available at URL: http://dspace.nbuv.gov.ua/handle/123456789/166246

zbMATH Keywords

Bernstein operatorGrüss-type inequalityCauchy mean-value theoremconvolution-type operatorsHermite-Fejér interpolation operator

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Inequalities for sums, series and integrals (26D15) Approximation by positive operators (41A36)

Related Items (44)

Approximation by modified Păltănea operators ⋮ Approximation on a new class of Szász-Mirakjan operators and their extensions in Kantorovich and Durrmeyer variants with applicable properties ⋮ Approximation properties by some modified Szasz-Mirakjan-Kantorovich operators ⋮ Genuine modified Bernstein-Durrmeyer operators ⋮ Approximation properties of \(\lambda\)-Kantorovich operators ⋮ New results concerning Chebyshev-Grüss-type inequalities via discrete oscillations ⋮ Convergence properties of certain positive linear operators ⋮ Convergence rate of Szász operators involving Boas-Buck-type polynomials ⋮ Unnamed Item ⋮ Quantitative \(q\)-Voronovskaya and \(q\)-Grüss-Voronovskaya-type results for \(q\)-Szász operators ⋮ q-Voronovskaya type theorems forq-Baskakov operators ⋮ Improvement of some inequalities of Chebysev-Grüss type ⋮ Asymptotic formulas for generalized Szász-Mirakyan operators ⋮ A generalized form of Grüss type inequality and other integral inequalities ⋮ Quantitative-Voronovskaya and Grüss-Voronovskaya type theorems for Szász-Durrmeyer type operators blended with multiple Appell polynomials ⋮ Approximation of functions by a class of Durrmeyer-Stancu type operators which includes Euler's beta function ⋮ Unnamed Item ⋮ The family of \(\lambda\)-Bernstein-Durrmeyer operators based on certain parameters ⋮ On the order of approximation by modified summation-integral-type operators based on two parameters ⋮ On Szász-Durrmeyer type modification using Gould Hopper polynomials ⋮ Voronovskaya Type Theorems in Weighted Spaces ⋮ Quantitative-Voronovskaja-type theorems for novel generalized-Szász-Durrmeyer operators incorporating the Sheffer sequences ⋮ Inequalities for Symmetrized or Anti-Symmetrized Inner Products of Complex-Valued Functions Defined on an Interval ⋮ Unnamed Item ⋮ On Pompeiu-Chebyshev functional and its generalization ⋮ Entropies and Heun functions associated with positive linear operators ⋮ Convergence of certain hybrid operators ⋮ Approximation by α-Bernstein-Schurer operator ⋮ Properties of discrete non-multiplicative operators ⋮ On the multiplicativity of linear operators ⋮ Quantitative Voronovskaya and Grüss-Voronovskaya type theorems for Jain-Durrmeyer operators of blending type ⋮ Quantitative Voronovskaya- and Grüss–Voronovskaya-type theorems by the blending variant of Szász operators including Brenke-type polynomials ⋮ The Product of Two Functions Using Positive Linear Operators ⋮ Classical Kantorovich operators revisited ⋮ Blending type approximation by modified Bernstein operators ⋮ Further results concerning some general Durrmeyer type operators ⋮ Approximation by modified \(U^{\rho }_n\) operators ⋮ Approximation by α-Bernstein-Schurer-Stancu operators ⋮ Extended Bernstein-Kantorovich-Stancu Operators with Multiple Parameters and Approximation Properties ⋮ Grüss and Grüss-Voronovskaya-type estimates for complex convolution polynomial operators ⋮ Quantitative theorems for a rich class of novel Miheşan-type approximation operators incorporating the Boas-Buck polynomials ⋮ GENUINE MODIFIED BASKAKOV-DURRMEYER OPERATORS ⋮ Quantitative Voronovskaya type results for a sequence of Stancu type operators ⋮ The new forms of Voronovskaya's theorem in weighted spaces

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• 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. \ .]
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