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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


A Study of Approximation Properties of Beta Type Summation-Integral Operator

Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 649--662 | DOI:10.5890/DNC.2021.12.006

Dhawal J. Bhatt$^{1,2}$, Vishnu Narayan Mishra$^{3}$ , Ranjan Kumar Jana$^{1}$

$^{1}$ Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath, Surat-395 007, Gujarat, India

$^{2}$ Present address: Department of Mathematics, St. Xavier's College, Navrangpura, Ahmedabad- 380 009, Gujarat, India

$^{3}$ Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur- 484 887, Madhya Pradesh, India

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In the present paper we introduce Durrmeyer-type operator involving the beta function and Baskakov basis function and study its approximation properties. We obtain the rate of convergence in different terms. The uniform convergence of sequence of these operators is achieved using Korovkin's theorem. Order of approximation for functions of some special class is also obtained. We establish the Voronovskaja type asymptotic result for this operator and a direct estimate of approximation for sequence of these operator.


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