Abstract
This paper is primarily concerned with multivariate Lupaş operator. We demonstrate that multivariate Lupaş operator preserves the properties of the general function of modulus of continuity, Lipschitz's constant and order of a Lipschitz continuous function. Moreover, we obtain monotonicity of the multivariate Lupaş operator under the condition that the original function is convex. Lastly, two modified extensions are constructed.
Keywords
Lupaş operator convexity Lipschitz continuity function of modulus of continuity monotonic convergence
References
- Agratini, O. On a sequence of linear and positive operators, Facta Univ. Ser. Math. Inform. 14 41-48, 1999.
- Aral, A., Inoan, D. and Raşa, I. On the generalized Szász-Mirakyan operators, Results Math.65 no. 3-4, 441-452, 2014 .
- Başcanbaz-Tunca,G., İnce-İlarslan, H. G. and Erençin, A. Bivariate Bernstein type operators , Appl. Math. Comput., 273 543-552, 2016.
- Cárdenas-Morales, D., Garrancho, P. and Rasa, I. Bernstein-type operators which preserve polynomials, Compt. Math. Appl. 62 158-163, 2011.
- Cao,F., Ding, C. and Xu, Z. On Multivariate Baskakov operator, J. Math. Anal. Appl. 307 no. 1, 274-291, 2005.
- Erençin, A., Başcanbaz-Tunca, G. and Taşdelen Yeşildal, F. Some properties of the operators de fined by Lupaş, Revue D'Analyse Numérique et de Théorie de L'Approximation, 43 no. 2, 158-164, 2014.
- Finta,Z. Quantitative estimates for some linear and positive operator, Studia Univ. Babeş- Bolyai Math. 47 no. 3, 71-84, 2002.
- Gadjiev, A.D. and Aral, A. The estimates of approximation by using a new type of weighted modulus of continuity, Computers and Mathematics with Applications 54 127-135, 2007 .
- Lupaş, A. The approximation by some positive linear operators In: Proceedings of the Inter- national Dortmund Meeting on Approximation Theory (M.W. Müller et al.,eds.),Akademie Verlag, Berlin, 201-229, 1995.
- Olgun, A. Some properties of the Multivariate Szász Operators, Comptes rendus de l'Acad emie bulgare des Sciences, 65, no. 2, 139-146, 2012.
- Sofonea, D. F. On a sequence of linear and positive operators, Results Math. 53 no. 3-4, 435-444, 2009.
Abstract
References
- Agratini, O. On a sequence of linear and positive operators, Facta Univ. Ser. Math. Inform. 14 41-48, 1999.
- Aral, A., Inoan, D. and Raşa, I. On the generalized Szász-Mirakyan operators, Results Math.65 no. 3-4, 441-452, 2014 .
- Başcanbaz-Tunca,G., İnce-İlarslan, H. G. and Erençin, A. Bivariate Bernstein type operators , Appl. Math. Comput., 273 543-552, 2016.
- Cárdenas-Morales, D., Garrancho, P. and Rasa, I. Bernstein-type operators which preserve polynomials, Compt. Math. Appl. 62 158-163, 2011.
- Cao,F., Ding, C. and Xu, Z. On Multivariate Baskakov operator, J. Math. Anal. Appl. 307 no. 1, 274-291, 2005.
- Erençin, A., Başcanbaz-Tunca, G. and Taşdelen Yeşildal, F. Some properties of the operators de fined by Lupaş, Revue D'Analyse Numérique et de Théorie de L'Approximation, 43 no. 2, 158-164, 2014.
- Finta,Z. Quantitative estimates for some linear and positive operator, Studia Univ. Babeş- Bolyai Math. 47 no. 3, 71-84, 2002.
- Gadjiev, A.D. and Aral, A. The estimates of approximation by using a new type of weighted modulus of continuity, Computers and Mathematics with Applications 54 127-135, 2007 .
- Lupaş, A. The approximation by some positive linear operators In: Proceedings of the Inter- national Dortmund Meeting on Approximation Theory (M.W. Müller et al.,eds.),Akademie Verlag, Berlin, 201-229, 1995.
- Olgun, A. Some properties of the Multivariate Szász Operators, Comptes rendus de l'Acad emie bulgare des Sciences, 65, no. 2, 139-146, 2012.
- Sofonea, D. F. On a sequence of linear and positive operators, Results Math. 53 no. 3-4, 435-444, 2009.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | August 1, 2018 |
| Published in Issue | Year 2018 Volume: 47 Issue: 4 |