• Title, Summary, Keyword: approximation theorem

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An Approximation Theorem for Two-Parameter Wiener Process

  • Kim, Yoon-Tae
    • Journal of the Korean Statistical Society
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    • v.26 no.1
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    • pp.75-88
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    • 1997
  • In this paper, a two-parameter version of Ikeda-Watanabe's mollifiers approximation of the Brownian motion is considered, and an approximation theorem corresponding to the one parameter case is proved. Using this approximation, we formulate Wong-Zakai type theorem is a Stochastic Differential Equation (SDE) driven by a two-parameter Wiener process.

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COMMON FIXED POINT THEOREM FOR OCCASIONALLY WEAKLY BAISED MAPPINGS AND ITS APPLICATION TO BEST APPROXIMATION

  • Deshpande, Bhavana;Chouhan, Suresh
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.543-552
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    • 2012
  • The aim of this paper is to prove a common fixed point theorem in normed linear spaces for discontinuous, occasionally weakly biased mappings without assuming completeness of the space. We give an example to illustrare our theorem. We also give an application of our theorem to best approximation theory. Our theorem improve the results of Gregus [9], Jungck [12], Pathak, Cho and Kang [22], Sharma and Deshpande [26]-[28].

STANCU TYPE GENERALIZATION OF MODIFIED GAMMA OPERATORS BASED ON q-INTEGERS

  • Chen, Shu-Ni;Cheng, Wen-Tao;Zeng, Xiao-Ming
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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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.

ON THE DEGREE OF APPROXIMATION FOR BIVARIATE LUPAS TYPE OPERATORS

  • Deo, Naokant
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1101-1116
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    • 2010
  • The aim of this paper is to give some simultaneous approximation properties as well as differential properties, Voronovskaya type theorem, several asymptotic formulae for the partial derivative and the degree of approximation for two dimensional Lupas type operators.

DEGREE OF APPROXIMATION TO A SMOOTH FUNCTION BY GENERALIZED TRANSLATION NETWORKS

  • HAHM, NAHMWOO;YANG, MEEHYEA;HONG, BUM IL
    • Honam Mathematical Journal
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    • v.27 no.2
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    • pp.225-232
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    • 2005
  • We obtain the approximation order to a smooth function on a compact subset of $\mathbb{R}$ by generalized translation networks. In our study, the activation function is infinitely many times continuously differentiable function but it does not have special properties around ${\infty}$ and $-{\infty}$ like a sigmoidal activation function. Using the Jackson's Theorem, we get the approximation order. Especially, we obtain the approximation order by a neural network with a fixed threshold.

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STATISTICAL A-SUMMABILITY OF DOUBLE SEQUENCES AND A KOROVKIN TYPE APPROXIMATION THEOREM

  • Belen, Cemal;Mursaleen, Mohammad;Yildirim, Mustafa
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.851-861
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    • 2012
  • In this paper, we define the notion of statistical A-summability for double sequences and find its relation with A-statistical convergence. We apply our new method of summability to prove a Korovkin-type approximation theorem for a function of two variables. Furthermore, through an example, it is shown that our theorem is stronger than classical and statistical cases.

Statistical Approximation of Szász Type Operators Based on Charlier Polynomials

  • Kajla, Arun
    • Kyungpook Mathematical Journal
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    • v.59 no.4
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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.