Topic
Baskakov operator
About: Baskakov operator is a research topic. Over the lifetime, 576 publications have been published within this topic receiving 10627 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
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1 Jan 1987
TL;DR: In this paper, the authors introduce a new way of measuring smoothness, which can also be described as a Peetre K functional between an Lp space and a weighted Sobolev space.
Abstract: The book introduces a new way of measuring smoothness. The need for this new concept arises from the failure of the classical moduli of smoothness to solve some basic problems, such as characterizing the behaviour of best polynomial approximation in Lp -1,1 . The new modulus, which has a simple form, can also be described as a Peetre K functional between an Lp space and a weighted Sobolev space. Connections between interpolation of spaces and approximation theory are utilized in applying the modulus of smoothness. The applications include best (weighted) polynomial approximation on a finite interval, characterization of the rate of approximation given by classical operator processes such as Bernstein, Kantorovich, Szasz-Mirakjan, and Post-Widder operators, Freud-type weighted polynomial approximation on infinite intervals with exponentially decreasing weights and polynomial approximation in several variables. Special emphasis is placed on the computability aspect of the moduli. The results are new, and complete proofs are given. It is hoped that the book will be of interest and useful for mathematicians working in approximation theory, interpolation of spaces, numerical analysis and real analysis.
1,231 citations
Book•
9 May 2013
TL;DR: The q-calculus as mentioned in this paper is a calculus of discrete operators and their results, including q-integral operators, q-Bernstein type integral operators and q-Summation integral operators.
Abstract: Introduction of q-calculus.- q-Discrete operators and their results.- q-Integral operators.- q-Bernstein type integral operators.- q-Summation-integral operators.- Statistical convergence of q-operators.- q-Complex operators.
410 citations
TL;DR: A sequence of positive linear operators which approximate each continuous function on [0, 1] while preserving the functione 2 (x) =x 2 is presented in this paper, where Quantitative estimates are given and are compared with estimates of approximation by Bernstein polynomials.
Abstract: A sequence of positive linear operators which approximate each continuous function on [0,1] while preserving the functione 2 (x) =x 2 is presented. Quantitative estimates are given and are compared with estimates of approximation by Bernstein polynomials. Connections with summability are discussed.
262 citations
TL;DR: This paper modify the definition of weighted statistical convergence and finds its relationship with the concept of statistical summability ( N ¯ , p n ) due to Moricz and Orhan (2004) to prove a Korovkin type approximation theorem.
178 citations
1 Jun 1999
TL;DR: In this article, it was shown that when the function is convex, the generalized Bernstein polynomials Bn are monotonic in n, as in the classical case.
Abstract: This paper is concerned with a generalization of the classical Bernstein polynomials where the function is evaluated at intervals which are in geometric progression. It is shown that, when the function is convex, the generalized Bernstein polynomials Bn are monotonic in n, as in the classical case.
150 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2024 | 22 |
| 2023 | 20 |
| 2022 | 25 |
| 2021 | 9 |
| 2020 | 12 |