Mathematics (Feb 2023)

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

  • Abdullah Alotaibi

DOI
https://doi.org/10.3390/math11041009
Journal volume & issue
Vol. 11, no. 4
p. 1009

Abstract

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In this paper, we construct the bivariate Szász–Jakimovski–Leviatan-type operators in Dunkl form using the unbounded sequences αn, βm and ξm 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.

Keywords