Browsing by Author "Cai, Q.B."

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    Scopus
    On the Properties of the Modified λ-Bernstein-Stancu Operators
    (Multidisciplinary Digital Publishing Institute (MDPI), 2024) Lin, Z.P.; Torun, G.; Kangal, E.; Kantar, Ü.D.; Cai, Q.B.
    In this study, a new kind of modified (Formula presented.) -Bernstein-Stancu operators is constructed. Compared with the original (Formula presented.) -Bézier basis function, the newly operator basis function is more concise in form and has certain symmetry beauty. The moments and central moments are computed. A Korovkin-type approximation theorem is presented, and the degree of convergence is estimated with respect to the modulus of continuity, Peetre’s K-functional, and functions of the Lipschitz-type class. Moreover, the Voronovskaja type approximation theorem is examined. Finally, some numerical examples and graphics to show convergence are presented.
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    Web of Science
    On the Properties of the Modified λ-Bernstein-Stancu Operators
    (2024.01.01) Lin, Z.P.; Torun, G.; Kangal, E.; Kantar, U.D.; Cai, Q.B.
    In this study, a new kind of modified lambda-Bernstein-Stancu operators is constructed. Compared with the original lambda-B & eacute;zier basis function, the newly operator basis function is more concise in form and has certain symmetry beauty. The moments and central moments are computed. A Korovkin-type approximation theorem is presented, and the degree of convergence is estimated with respect to the modulus of continuity, Peetre's K-functional, and functions of the Lipschitz-type class. Moreover, the Voronovskaja type approximation theorem is examined. Finally, some numerical examples and graphics to show convergence are presented.