Weighted approximations by sampling type operators: recent and new results

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Constructive Mathematical Analysis
Volume:7 Issue:3
Weighted approximations by sampling type operators: recent and new results

Weighted approximations by sampling type operators: recent and new results

Pages : 114-125

View : 94 | Download : 69

Publication Date : 2024-09-15

Article Type : Research Paper

Abstract :In this paper, we collect some recent results on the approximation properties of generalized sampling operators and Kantorovich operators, focusing on pointwise and uniform convergence, rate of convergence, and Voronovskaya-type theorems in weighted spaces of functions. In the second part of the paper, we introduce a new generalization of sampling Durrmeyer operators including a special function $\\rho$ which satisfies certain assumptions. For the family of newly constructed operators, we obtain pointwise convergence, uniform convergence and rate of convergence for functions belonging to weighted spaces of functions.
Keywords : Sampling series, generalized sampling operator, Kantorovich operator, Durrmeyer type sampling operator, weighted approximation

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