Baskakov operators and Jacobi weights: pointwise estimates

Jorge Bustamante,Juan Jesús Merino-García,José María Quesada

doi:10.1186/s13660-021-02653-4

Abstract

In this paper we present direct results (upper estimates) for Baskakov operators acting in spaces related with Jacobi-type weights. Our results include and extend some known facts related with this problem. The approach is based in the use of a new pointwise K-functional.

Highlights

Let C[0, ∞) be the family of all real continuous functions on the semiaxis and B(0, ∞) the family of all bounded functions in (0, ∞)
Some authors have considered these operators acting in spaces defined with the help of a Jacobi weight in the discrete case (λ = n ∈ N). √
In this paper we present upper estimates for the error (x)|f (x) – Vλ(f, x)| assuming that a ≥ –1 and b ∈ R

Summary

Introduction

Let C[0, ∞) be the family of all real continuous functions on the semiaxis and B(0, ∞) the family of all bounded functions in (0, ∞). Some authors have considered these operators acting in spaces defined with the help of a Jacobi weight in the discrete case (λ = n ∈ N) (see [6, 17, 18], and [21]). The use of a continuous parameter allows us to apply the results to study other family of operators.

Results

Conclusion