Browsing by Author "Cai, Qing-Bo"

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Approximation by a New Stancu Variant of Generalized (Λ, Μ)-Bernstein Operators
(Elsevier, 2024) Cai, Qing-Bo; Aslan, Resat; Ozger, Faruk; Srivastava, Hari Mohan
The primary objective of this work is to explore various approximation properties of Stancu variant generalized (lambda, mu)-Bernstein operators. Various moment estimates are analyzed, and several aspects of local direct approximation theorems are investigated. Additionally, further approximation features of newly defined operators are delved into, such as the Voronovskaya-type asymptotic theorem and pointwise estimates. By comparing the proposed operator graphically and numerically with some linear positive operators known in the literature, it is evident that much better approximation results are achieved in terms of convergence behavior, calculation efficiency, and consistency. Finally, the newly defined operators are used to obtain a numerical solution for a special case of the fractional Volterra integral equation of the second kind.
On a New Kind of Λ-Bernstein Operators for Univariate and Bivariate Functions
(Univ Nis, Fac Sci Math, 2025) Cai, Qing-Bo; Kangal, Esma; Kantar, Ulku Dinlemez; Zhou, Guorong; Asian, Resat
This paper presents a novel class of lambda-Bernstein operators, wherein the parameter lambda is an element of [-1, 1]. An approximation theorem of the Korovkin type is explored, a local approximation theorem is established and an asymptotic formula of the Voronovskaja type is derived. In addition, the bivariate tensor product operators are built, some approximation properties are discussed, including an asymptotic theorem of the Voronovskaja type and the order of convergence in relation to Peetre's K-functional. Finally, for certain continuous functions, numerical examples and plots to demonstrate our newly defined operators' convergence behavior are provided and there are also provided in comparison with the classical Kantorovich operators in terms of the approximation error.