Inverse approximation and GBS of bivariate Kantorovich type sampling series

Abstract

In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for f ∈ C 2 (R 2 ) (the space of all continuous functions with upto second order partial derivatives are continuous and bounded on R 2 ). Further, we prove the rate of approximation in the Bögel space of continuous functions for the GBS (Generalized Boolean Sum) of these operators. Finally, we give some examples for the kernel to which the theory can be applied.Keywords Inverse result · Bivariate Kantorovich type Sampling series · Rate of convergence · GBS operators · mixed modulus of smoothnesswhere w > 0 and (x, y) ∈ R 2 . These operators have great importance in the development of models for signal recovery. These type of operators have been

On the Approximation Properties of q − Analogue Bivariate λ -Bernstein Type Operators

“…Recently, Kajla and Miclacus [16] studied the rate of approximation of Bögel continuous and Bögel differentiable functions by the GBS operators of Bernstein-Durrmeyer type operators. In the last year, Kumar and Shivam [26] constructed the bivariate Kantorovich-type sampling operator, involved with GBS operators, as well as estimation of the rate of convergence of the sequences of these operators.…”

On Bivariate Kantorovich Exponential Sampling Series

“…Agrawal et al [3] derived the order of convergence for Lupas ¸-Durrmeyer type GBS operators on the basis of Pólya distribution. Since then, various authors have contributed significantly in this direction, see eg [2,17,36,44,38,42,1].…”

On Approximation by Kantorovich Exponential Sampling Operators

“…In the last few decades, the Kantorovich modifications of several operators have been constructed and analyzed, eg. [5,7,9,25,29,31,36,35,1,33,2]. We also refer some of the recent developments related to the theory of exponential sampling, see [16,12,17,3,18,34].…”