On the preservation of log convexity and log concavity under some classical Bernstein-type operators

DOI10.1016/j.jmaa.2009.06.075zbMath1178.41015OpenAlexW2157783951MaRDI QIDQ1034568

Francisco German Badía

Publication date: 6 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.06.075

zbMATH Keywords

Bernstein operatorsBaskakov operatorsSzasz operatorsGamma type operators and Weierstrass operatorslog concavityLog convexity

Mathematics Subject Classification ID

Approximation by positive operators (41A36)

Related Items (8)

PRESERVATION OF LOG-CONCAVITY AND LOG-CONVEXITY UNDER OPERATORS ⋮ Conditions on unimodality and logconcavity for densities of coherent systems with an application to Bernstein operators ⋮ Log-concavity preserving property of Bernstein operators and Bernstein semigroup ⋮ Log concavity preservation by beta operator based on probability tools ⋮ Three kinds of convexity and concavity properties of optimal value function in parametric nonlinear programming ⋮ Preservation of ageing classes in deterioration models with independent increments ⋮ PRESERVATION PROPERTIES OF A RENEWAL PROCESS STOPPED AT A RANDOM DEPENDENT TIME ⋮ Log-concavity for Bernstein-type operators using stochastic orders

Cites Work

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• On the approximation of convex functions by Bernstein-type operators
• Logconcavity versus logconvexity: A complete characterization
• Beta-type operators preserve shape properties
• On the monotonicity of positive linear operators
• On uniform approximation by some classical Bernstein-type operators.
• Some probabilistic methods in the theory of approximation operators
• PRESERVATION OF RELIABILITY CLASSES UNDER MIXTURES OF RENEWAL PROCESSES
• Approximation of Functions by a Bernstein-Type Operator
• Upper estimates in direct inequalities for Bernstein-type operators

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