• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.15-28
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• 2018

In this paper, we introduce a Stancu type generalization of genuine LupaŞ-Beta operators of integral type. We establish some moment estimates and the direct results in terms of classical modulus of continuity, Voronovskaja-type asymptotic theorem, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Lastly, we propose a king type modification of these operators to obtain better estimates.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.531-542
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• 2002

In this paper we deal with a sequence of positive linear operators ${{R_n}}^{[$\beta$]}$ approximating functions on the unbounded interval [0, $\infty$] which were firstly used by K. balazs and J. Szabados. We give pointwise estimates in the framework of polynomial weighted function spaces. Also we establish a Voronovskaja type theorem in the same weighted spaces for ${{K_n}}^{[$\beta$]}$ operators, representing the integral generalization in Kantorovich sense of the ${{R_n}}^{[$\beta$]}$.

• 대한수학회보
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• 제54권2호
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• pp.359-373
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• 2017

In this paper, we propose the Stancu type generalization of a kind of modified q-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.679-688
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• 2019

In the present note, we study some approximation properties of the Szász type operators based on Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). We establish the rates of A-statistical convergence of these operators. Finally, we prove a Voronovskaja type approximation theorem and local approximation theorem via the concept of A-statistical convergence.