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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 47 Issue: 4

On multivariate Lupaş operators

Murat Bodur
Fatma Taşdelen
Gülen Başcanbaz-tunca
Pages
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Publication Date
2018-08-01
DOI
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⚡ TL;DR(Too Long; Didn't Read)

Lastly, two modified extensions are constructed.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper is primarily concerned with multivariate Lupaş operator.
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Key Findings & Data: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.
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Conclusion & Impact:Lastly, two modified extensions are constructed.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lupaş operator · convexity · Lipschitz continuity

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.

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Cite This Article

Bodur, M., Taşdelen, F., Başcanbaz-tunca, G. (2018). On multivariate Lupaş operators. Hacettepe Journal of Mathematics and Statistics, Volume: 47 Issue: 4. https://ajindex.com/articles/1402903

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References (14)

  1. Agratini, O. On a sequence of linear and positive operators, Facta Univ. Ser. Math. Inform. 14 41-48, 1999.
  2. Aral, A., Inoan, D. and Raşa, I. On the generalized Szász-Mirakyan operators, Results Math.65 no. 3-4, 441-452, 2014.
  3. Başcanbaz-Tunca,G., İnce-ݝlarslan, H. G. and Erençin, A. Bivariate Bernstein type operators, Appl. Math. Comput., 273 543-552, 2016.
  4. Cárdenas-Morales, D., Garrancho, P. and Rasa, I. Bernstein-type operators which preserve polynomials, Compt. Math. Appl. 62 158-163, 2011.
  5. Cao,F., Ding, C. and Xu, Z. On Multivariate Baskakov operator, J. Math. Anal. Appl. 307 no. 1, 274-291, 2005.
  6. Erençin, A., Başcanbaz-Tunca, G. and Taşdelen Yeşildal, F. Some properties of the operators defined by Lupaş, Revue D'Analyse Numérique et de Théorie de L'Approximation, 43 no. 2, 158-164, 2014.
  7. Finta,Z. Quantitative estimates for some linear and positive operator, Studia Univ. Babeş- Bolyai Math. 47 no. 3, 71-84, 2002.
  8. 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.
  9. 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.
  10. Olgun, A. Some properties of the Multivariate Szász Operators, Comptes rendus de l'Acad emie bulgare des Sciences, 65, no. 2, 139-146, 2012.
  11. Sofonea, D. F. On a sequence of linear and positive operators, Results Math. 53 no. 3-4, 435-444, 2009.
  12. Aral, A., Inoan, D. and Raşa, I. On the generalized Szász-Mirakyan operators, Results Math.65 no. 3-4, 441-452, 2014.
  13. Başcanbaz-Tunca,G., İnce-ݝlarslan, H. G. and Erençin, A. Bivariate Bernstein type operators, Appl. Math. Comput., 273 543-552, 2016.
  14. 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.