• 제목/요약/키워드: $Sz{\acute{a}}sz$ operator

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Statistical Approximation of Szász Type Operators Based on Charlier Polynomials

  • Kajla, Arun
    • 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.

Szász-Kantorovich Type Operators Based on Charlier Polynomials

  • Kajla, Arun;Agrawal, Purshottam Narain
    • Kyungpook Mathematical Journal
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    • 제56권3호
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    • pp.877-897
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    • 2016
  • In the present article, we study some approximation properties of the Kantorovich type generalization of $Sz{\acute{a}}sz$ type operators involving Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A-statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.

ON 𝜃-MODIFICATIONS OF GENERALIZED TOPOLOGIES VIA HEREDITARY CLASSES

  • Al-Omari, Ahmad;Modak, Shyamapada;Noiri, Takashi
    • 대한수학회논문집
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    • 제31권4호
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    • pp.857-868
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    • 2016
  • Let (X, ${\mu}$) be a generalized topological space (GTS) and $\mathcal{H}$ be a hereditary class on X due to $Cs{\acute{a}}sz{\acute{a}}r$ [8]. In this paper, we define an operator $()^{\circ}:\mathcal{P}(X){\rightarrow}\mathcal{P}(X)$. By setting $c^{\circ}(A)=A{\cup}A^{\circ}$ for every subset A of X, we define the family ${\mu}^{\circ}=\{M{\subseteq}X:X-M=c^{\circ}(X-M)\}$ and show that ${\mu}^{\circ}$ is a GT on X such that ${\mu}({\theta}){\subseteq}{\mu}^{\circ}{\subseteq}{\mu}^*$, where ${\mu}^*$ is a GT in [8]. Moreover, we define and investigate ${\mu}^{\circ}$-codense and strongly ${\mu}^{\circ}$-codense hereditary classes.