Abstract
We have constructed a new sequence of positive linear operators with two variables by using Szasz-Kantorovich-Chlodowsky operators and Brenke polynomials. We give some inequalities for the operators by means of partial and full modulus of continuity and obtain a Lipschitz type theorem. Furthermore, we study the convergence of Szasz-Kantorovich-Chlodowsky-Brenke operators in weighted space of function with two variables and estimate the rate of approximation in terms of the weighted modulus of continuity.
Highlights
The well-known Mirakjan-Favard-Szasz type operators of one variable are defined as Sn (f; x) = ∞ ∑ωni f i=0 ( i n ), n ∈ N, x ∈ [0, ∞), (1)where ωni (x) e−nxi i!
We studied a new sequence generalization of the SzaszKantorovich-Chlodowsky type operators defined by means of the Brenke type polynomials defined by (9)
We mentioned results on the weighted modulus of continuity due to Ispir for the operators Tnb,mm,c,man
Summary
The well-known Mirakjan-Favard-Szasz type operators of one variable are defined as. and f : [0, ∞) → R is such that the above exist series. In [9, 10] authors introduced a bivariate blending variant of the Szasz type operators and studied local approximation properties for these operators. They estimated the approximation order in terms of Peetre’s K-functional and partial moduli of continuity. Chlodowsky operators based on Brenke polynomials as follows: Tnb,mm,c,man (f; x, y) anK ncm (1) L (bm y). We study the linear positive operators in a weighted space of function with two variables and estimate the rate of approximation of the operators Tnb,mm,c,man in the terms of the weighted modulus of continuity
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