A Generalization of The Baskakov-Kantorovich Sequence Based on Two Nonnegative Parameters
DOI:
https://doi.org/10.56714/bjrs.51.2.14Keywords:
Ordinary Approximation Theory, Baskakov Operators, Α-Baskakov-Kantorovich Operators, Voronovsky-Type Asymptotic FormulaAbstract
This paper introduces a generalized sequence of linear positive operators, denoted the -Baskakov-Kantorovich sequence, which extends the classical Baskakov-Kantorovich sequence by introducing two nonnegative parameters, and . These parameters enhance the flexibility of this sequence, enabling finer control over the approximation process. Convergence of the sequence to any continuous function on nonnegative real numbers is established using Korovkin’s theorem. Furthermore, a Voronovsky-type asymptotic formula is derived, providing insight into the order of convergence as tends to infinity. To support the theoretical results, a numerical example is presented in which the sequence is applied to approximate a test function. The numerical findings indicate that the proposed operators not only improve approximation accuracy but also reveal flexibility in handling different types of parameterized test functions, underscoring their potential as a more versatile and effective tool in approximation theory. This study contributes to the development of parametric generalizations of classical operators with enhanced approximation properties
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