Shape preserving properties of univariate Lototsky-Bernstein operators
The main goal of the present paper is to study shape preserving properties of univariate Lototsky-Bernstein operators, which are based on Lototsky-Bernstein basis functions. The Lototsky-Bernstein basis functions \(b_{n,k} (x)\) (\(0 \leq k\leq n\)) of order \(n\) are constructed by replacing \(x\) in the \(i\)th factor of the generating function for the classical Bernstein basis functions of degree \(n\) by a continuous nondecreasing function \(p_i (x)\), where \(p_i (0) = 0\) and \( p_i (1) = 1\) for \(1 \leq i \leq n\). Here the authors have established some very interesting shape preserving properties of these Lototsky-Bernstein operators. Such a nice paper is a new direction for researchers working on linear positive operators.
scientific article; zbMATH DE number 6801960
scientific article