Yazar "Mohiuddine, S. A." seçeneğine göre listele

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    Approximation by (p, q)-Baskakov-Durrmeyer-Stancu Operators
    (Springer Basel Ag, 2018) Acar, Tuncer; Mohiuddine, S. A.; Mursaleen, Mohammad
    The present paper deals with the Stancu-type generalization of (p, q)-Baskakov-Durrmeyer operators. We investigate local approximation, weighted approximation properties of new operators and present the rate of convergence by means of suitable modulus of continuity. At the end of the paper, we introduce a new modification of (p, q)-Baskakov-Durrmeyer-Stancu operators with King approach.
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    Approximation by Bivariate (p, q)-Bernstein-Kantorovich Operators
    (Springer International Publishing Ag, 2018) Acar, Tuncer; Aral, Ali; Mohiuddine, S. A.
    In the present paper, we introduce Kantorovich modifications of (p, q)-Bernstein operators for bivariate functions using a new (p, q)-integral. We first estimate the moments and central moments. We give the uniform convergence of new operators, rate of convergence in terms of modulus of continuity. The approximations behaviours of the operators for functions having continuous partial derivatives and for functions belong to Lipschitz class are investigated as well.
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    Construction of a new family of Bernstein-Kantorovich operators
    (Wiley, 2017) Mohiuddine, S. A.; Acar, Tuncer; Alotaibi, Abdullah
    In the present paper, we construct a new sequence of Bernstein-Kantorovich operators depending on a parameter alpha. The uniform convergence of the operators and rate of convergence in local and global sense in terms of first- and second-order modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our construction are obtained. The last section is devoted to bivariate generalization of Bernstein-Kantorovich operators and their approximation behaviors.
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    On Kantorovich Modification of (p, q)-Bernstein Operators
    (Springer International Publishing Ag, 2018) Acar, Tuncer; Aral, Ali; Mohiuddine, S. A.
    In the present paper, we introduce Kantorovich modifications of (p, q)-Bernstein operators using a new (p, q) -integral. We first estimate the moments and central moments. We obtain uniform convergence of new operators, rate of convergence in terms of classical modulus of continuity and second order modulus of continuity. We also investigate the rate of convergence of new operators for functions belonging to Lipschitz class and finally, we give an upper bound for the error of approximation via modulus of continuity of the derivative of approximating function.
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    Statistical (C, 1) (E, 1) Summability and Korovkin's Theorem
    (Univ Nis, Fac Sci Math, 2016) Acar, Tuncer; Mohiuddine, S. A.
    Korovkin-type approximation theory usually deals with convergence analysis for sequences of positive operators. This approximation theorem was extended to more general space of sequences via different way such as statistical convergence, summation processes. In this work, we introduce a new type of statistical product summability, that is, statistical (C, 1) (E, 1) summability and further apply our new product summability method to prove Korovkin type theorem. Furthermore, we present a rate of convergence which is uniform in Korovkin type theorem by statistical (C, 1) (E, 1) summability.