SUMMATION-INTEGRAL BERNSTEIN TYPE OF NEURAL NETWORK OPERATORS

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Published: 2017-10-25

Page: 74-86


ALI J. MOHAMMAD *

Department of Mathematics, College of Education for Pure Science, University of Basrah, Basrah, Iraq.

IBTIHAL JASSIM MOHAMMAD

Department of Mathematics, College of Education for Pure Science, University of Basrah, Basrah, Iraq.

*Author to whom correspondence should be addressed.


Abstract

In this paper, we introduce a family of neural network operators of summation-integral Bernstein type, which are define by using some sigmoidal functions. We give pointwise and uniform approximation theorems for these operators when are applied for continuous functions. In addition, we discuss the approximation for these operators in -spaces with . Then we give some applications of the sequences of a family of linear positive multivariate neural network operators , then we describe the results by graphics of the error function for some particular values of  and for two test functions in -dimensional.

Keywords: Sigmoidal functions, multivariate neural network, uniform approximation, L^p-approximation, Summation-integral Bernstein-type.


How to Cite

MOHAMMAD, A. J., & MOHAMMAD, I. J. (2017). SUMMATION-INTEGRAL BERNSTEIN TYPE OF NEURAL NETWORK OPERATORS. Asian Journal of Mathematics and Computer Research, 21(2), 74–86. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1120

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