Approximation properties of a certain nonlinear Durrmeyer operators

The present paper is concerned with a certain sequence of the nonlinear Durrmeyer operators ND_{n}, very recently introduced by the author karslipam and karslibimj , of the form (ND_{n}f)(x)=∫₀¹K_{n}(x,t,f(t))dt,0≤x≤1,n∈N, acting on Lebesgue measurable functions defined on [0,1], where K_{n}(x,t,u)=F_{n}(x,t)H_{n}(u) satisfy some suitable assumptions. As a continuation of the very recent papers of the author karslipam and karslibimj , 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.