On bivariate Jain operators

Münüse Akçay; Gülen Başcanbaz-Tunca

doi:10.3934/mfc.2021026

Article Contents

2022, Volume 5, Issue 3: 173-185. Doi: 10.3934/mfc.2021026

This issue Previous Article A new kind of Bi-variate $ \lambda $ -Bernstein-Kantorovich type operator with shifted knots and its associated GBS form Next Article Convergence of modified Szász-Mirakyan-Durrmeyer operators depending on certain parameters

On bivariate Jain operators

Münüse Akçay and
Gülen Başcanbaz-Tunca^,

Ankara University, Faculty of Science, Department of Mathematics, Str. Dögol, 06100, Beşevler, Ankara, Turkey

^* Corresponding author: Gülen Başcanbaz-Tunca
^* Corresponding author: Gülen Başcanbaz-Tunca

Received: May 31, 2021

Revised: August 31, 2021

Early access: October 2021

Published: August 2022

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Abstract

In this paper we deal with bivariate extension of Jain operators. Using elementary method, we show that these opearators are non-increasing in $ n $ when the attached function is convex. Moreover, we demonstrate that these operators preserve the properties of modulus of continuity. Finally, we present a Voronovskaja type theorem for the sequence of bivariate Jain operators.

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Mathematics Subject Classification: Primary: 41A25, 41A36; Secondary: 41A63.

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