Approximation Properties of a Certain Nonlinear Durrmeyer Operators

Harun Karsli


The present paper is concerned with a certain sequence of the nonlinear Durrmeyer operators ND_{n}, very recently introduced by the author <cite>karslipam</cite> and <cite>karslibimj</cite>, of the form


acting on Lebesgue measurable functions defined on [0,1], where


satisfy some suitable assumptions. As a continuation of the very recent papers of the author <cite>karslipam</cite> and <cite>karslibimj</cite>, we estimate their pointwise convergence to functions f and ψ∘|f| having derivatives are of bounded (Jordan) variation on the interval [0,1].Here ψo|f| denotes the composition of the functions ψ and |f|. The function ψ:R₀⁺→R₀⁺ is continuous and concave with ψ(0)=0, ψ(u)>0 for u>0.This study can be considered as an extension of the related results dealing with the classical Durrmeyer operators.

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