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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


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Approximation by modified Jain–Baskakov operators

Vishnu Narayan MishraORCID iD: https://orcid.org/0000-0002-2159-7710
  • Corresponding author
  • Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484-887; and L. 1627 Awadh Puri Colony Beniganj, Phase III, Opposite – Industrial Training Institute (I.T.I.), Ayodhya Main Road Faizabad 224-001, (Uttar Pradesh), India
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/ Preeti Sharma / Marius Mihai Birou
Published Online: 2019-02-16 | DOI: https://doi.org/10.1515/gmj-2019-2008

Abstract

In the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameter c. The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which preserves the test functions e0 and e1. It is shown that these King type operators provide a better approximation order than some Baskakov–Durrmeyer operators for continuous functions defined on some closed intervals.

Keywords: Jain operators; Baskakov operators; King type operators; weighted approximation

MSC 2010: 41A25; 41A36

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About the article

Received: 2017-04-15

Revised: 2017-10-26

Accepted: 2017-11-08

Published Online: 2019-02-16


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2008.

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