Abstract
In this article, we propose a different generalization of ( p , q ) -BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where ( p , q ) -integers contains symmetric property. We establish a Korovkin approximation theorem in the statistical sense and obtain the statistical rates of convergence. Furthermore, we also introduce a bivariate extension of proposed operators and carry many statistical approximation results. The extra parameter p plays an important role to symmetrize the q-BBH operators.
Highlights
IntroductionGadjiev and Çakar [3] established the Korovkin type theorem which gives the convergence for the sequence of linear positive operators (LPO) to the functions in Hω
The q-analog of Bleiman, Butzer and Hahn operators (BBH) [1] is defined by: q Ln ( f ; x ) = qn ( x ) n ∑k =0 f [k ]q [ n − k + 1] q q k ! q k ( k −1) " n k #
Gadjiev and Çakar [3] established the Korovkin type theorem which gives the convergence for the sequence of linear positive operators (LPO) to the functions in Hω
Summary
Gadjiev and Çakar [3] established the Korovkin type theorem which gives the convergence for the sequence of linear positive operators (LPO) to the functions in Hω. The ( p, q)-analogue of BBH operators was introduced by Mursaleen et al in [20] as follows:. Authors established different approximation properties of the sequence of operators (3). Mursaleen and Nasiruzzaman constructed bivariate ( p, q)-BBH operators [21] and studied many nice properties based on that sequence of operators and given some generalization of that sequence of bivariate operators introducing one more parameter γ in the operators.
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