Iterates of <i>q</i>-Bernstein operators on triangular domain with all curved sides-Reference-Cited by-同舟云学术

Iterates of q-Bernstein operators on triangular domain with all curved sides

Published:2022-01-01 Issue:1 Volume:55 Page:891-899
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Iliyas Mohammad¹,Khan Asif¹,Arif Mohd¹²,Mursaleen Mohammad¹³,Lone Mudassir Rashid¹²

Affiliation:

1. Department of Mathematics, Aligarh Muslim University , Aligarh 202002 , India

2. Department of Mathematical Sciences, Baba Ghulam Shah Badshah University , Rajouri-185234 , India

3. Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan) , Taichung , Taiwan

Abstract

Abstract In this article, Phillips-type Bernstein operators

( ℬ m , q t F ) ( t , s )

({{\mathcal{ {\mathcal B} }}}_{m,q}^{t}F)\left(t,s)

and

( ℬ n , q s F ) ( t , s )

({{\mathcal{ {\mathcal B} }}}_{n,q}^{s}F)\left(t,s)

, their products, and Boolean sum based on q-integer have been studied on a triangle with all curved sides. Furthermore, convergence of iterates of these operators have been analyzed using the weakly Picard operators technique and the contraction principle.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0173/pdf

Reference39 articles.

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2. K. Weierstrass, Über die analytische darstellbarkit sogenannter willkürlicher functionen einer reelen varänderlichen sitzungsberichtedr, Koniglish Preussicschen Akademie der Wissenschcaften zu Berlin, Vol. 633–639, 1885, pp. 789–805.

3. A. Lupas, A q-analogue of the Berstein operater, Seminar on Numerical and Statistiacal, Calculus, University of Cluj-Napoca, Vol. 9, 1987, pp. 85–92.

4. G. M. Phillips, Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1885), 511–518.

5. G. M. Phillips, A generalization of the Berstein polynomials based on the q-integers, Anziam J. 42 (2000), no. 1, 79–86.

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