On convergence of positive linear operators related to squared-Durrmeyer operators

I. Tiryaki

The aim of this paper is to study the pointwise behavior of certain sequences of the squared-Durrmeyer operators DB_n² and ĎB_n² acting on bounded functions on an interval [0, 1], defined by Gavrea and Ivan. Here we estimate the rate of convergence at a point y, which is a Lebesgue point of g ∈ L₁([0, 1]) be such that ψo|g| ∈ BV([0, 1]), where ψo|g| denotes the composition of the functions ψ and |g|. The function ψ:ℝ₀⁺ → ℝ₀⁺ is continuous and concave with ψ(0)=0, ψ(u)>0 for u>0, which appears from the (L - ψ) Lipschitz conditions.

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16,  supplement issue 3 (2023), pp. 45-58