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  • Küçük Resim
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    General Gamma type operators based on q-integers
    (Elsevier Science Inc, 2015) Karslı, Harun; Agrawal, P. N.; Goyal, Meenu
    In the present paper, we introduce the q-analogue of the general Gamma type operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimate using the Lipschitz type maximal function. Further, we study the A-statistical convergence of these operators. Lastly, we propose a king type modification of these operators to obtain better estimates. (C) 2014 Elsevier Inc. All rights reserved.
  • Küçük Resim
    Öğe
    Szasz-Baskakov type operators based on q-integers
    (Springer International Publishing Ag, 2014) Agrawal, Purshottam N.; Karslı, Harun; Goyal, Meenu
    In the present paper, we introduce the q-analog of the Stancu variant of Szasz-Baskakov operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then we obtain a point-wise estimate using the Lipschitz type maximal function. Lastly, we study the A-statistical convergence of these operators and also, in order to obtain a better approximation, we study a King type modification of the above operators.