On the Approximation by Bivariate Szász–Jakimovski–Leviatan-Type Operators of Unbounded Sequences of Positive Numbers

In this paper, we construct the bivariate Szász–Jakimovski–Leviatan-type operators in Dunkl form using the unbounded sequences <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mi&g...

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Bibliographic Details
Main Author: Abdullah Alotaibi
Format: Article
Language:English
Published: MDPI AG 2023-02-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/11/4/1009
Description
Summary:In this paper, we construct the bivariate Szász–Jakimovski–Leviatan-type operators in Dunkl form using the unbounded sequences <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mi>n</mi></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mi>m</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ξ</mi><mi>m</mi></msub></semantics></math></inline-formula> of positive numbers. Then, we obtain the rate of convergence in terms of the weighted modulus of continuity of two variables and weighted approximation theorems for our operators. Moreover, we provide the degree of convergence with the help of bivariate Lipschitz-maximal functions and obtain the direct theorem.
ISSN:2227-7390