Browsing by Author "Alotaibi, Abdullah"

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    Bézier-summation-integral-type operators that include Pólya–Eggenberger distribution
    (Mathematics, 2022) Mohiuddine, Sayed Abdul; Kajla, Arun; Alotaibi, Abdullah
    We define the summation-integral-type operators involving the ideas of Pólya–Eggenberger distribution and Bézier basis functions, and study some of their basic approximation properties. In addition, by means of the Ditzian–Totik modulus of smoothness, we study a direct theorem as well as a quantitative Voronovskaja-type theorem for our newly constructed operators. Moreover, we investigate the approximation of functions with derivatives of bounded variation (DBV) of the aforesaid operators.
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    Durrmeyer-Type Generalization of -Bernstein Operators
    (Mathematics, 2022) Kajla, Arun; Mohiuddine, S,A; Alotaibi, Abdullah
    In the present manuscript, we consider -Bernstein-Durrmeyer operators involving a strictly positive continuous function. Firstly, we prove a Voronovskaja type, quantitative Voronovskaja type and Gr¨ uss-Voronovskaja type asymptotic formula, the rate of convergence by means of the modulus of continuity and for functions in a Lipschitz type space. Finally, we show that the numerical examples which describe the validity of the theoretical example and the effectiveness of the defined operators.