Shape preserving properties of univariate Lototsky-Bernstein operators
type: Item
instance of: scholarly article
title: Shape preserving properties of univariate Lototsky-Bernstein operators
zbMATH Open document ID: 1376.41010
author: Xiaowei Xu
author: Xiao-Ming Zeng
author: Ron Goldman
published in: Journal of Approximation Theory
publication date: 2017-11-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 6801960
zbMATH Keywords: Lototsky-Bernstein operators
zbMATH Keywords: shape preservation
zbMATH Keywords: total positivity
zbMATH Keywords: iterates
zbMATH Keywords: fixed point
MaRDI profile type: Publication
full work available at URL: j.jat.2017.09.002
OpenAlex ID: W2754042113
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DOI: 10.1016/J.JAT.2017.09.002
description: scientific article; zbMATH DE number 6801960