Abstract
In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for $$ f \in C^{(2)}({\mathbb {R}}^{2})$$ (the space of all continuous functions with upto second order partial derivatives are continuous and bounded on $$ {\mathbb {R}}^{2}).$$ Further, we introduce the generalized Boolean sum (GBS) operators of bivariate Kantorovich type sampling series. We also study the rate of approximation for the GBS operators in terms of mixed modulus of smoothness and mixed K-functionals for the space of Bogel-continuous functions. Finally, we give some examples for the kernel to which the theory can be applied along with the graphical representations.
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More From: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
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