Some properties of the operators defined by Lupaș

Authors

  • Ayşegül Erençin Abant Izzet Baysal University, Turkey
  • Gülen Bașcanbaz-Tunca Ankara University, Turkey
  • Fatma Tașdelen Ankara University, Turkey

DOI:

https://doi.org/10.33993/jnaat432-1027

Keywords:

orthogonal polynomials, spectral method, error estimate, condition number, programming, Lupas operator
Abstract views: 388

Abstract

In the present paper, we show that a subclass of the operators defined by Lupaș [12] preserve properties of the modulus of continuity function and Lipschitz constant and the order of a Lipschitz continuous function. We are also concerned with the monotonicity of a sequence of such operators for convex functions.

Downloads

Download data is not yet available.

References

U. Abel and M. Ivan, On a generalization of an approximation operator defined by A. Lupaş, Gen. Math., 15 (2007) no. 1, pp. 21-34.

T. Acar and A. Aral, Approximation properties of two dimensional Bernstein-Stancu-Chlodowsky operators, Matematiche (Catania), 68 (2013) no. 2, pp. 15-31, http://dx.doi.org/10.4418/2013.68.2.2

O. Agratini, On a sequence of linear positive operators, Facta Univ. Ser. Math. Inform., 14 (1999), pp. 41-48.

B. M. Brown, D. Elliott and D.F. Paget, Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory, 49 (1987) no. 2, pp. 196-199, http://dx.doi.org/10.1016/0021-9045(87)90087-6 DOI: https://doi.org/10.1016/0021-9045(87)90087-6

F. Dirik, Statistical convergence and rate of convergence of a sequence of positive linear operators, Math. Commun., 12 (2007) no. 2, pp. 147-153.

A. Erençin and F. Taşdelen, On a family of linear and positive operators in weighted spaces, JIPAM. J. Inequal. Pure Appl. Math., 8 (2007) no. 2, Article 39, 6 pp.

A. Erençin and F. Taşdelen, On certain Kantorovich type operators, Fasc. Math., (2009) no. 41, pp. 65-71.

A. Erençin, G. Başcanbaz-Tunca and F. Taşdelen, Some preservation properties of MKZ-Stancu type operators, Sarajevo J. Math., 10 (22) (2014) no. 1, pp. 93-102. DOI: https://doi.org/10.5644/SJM.10.1.12

G.C. Jain and S. Pethe, On the generalizations of Bernstein and Szasz-Mirakjan operators, Nanta Math., 10 (1977) no. 2, pp. 185-193.

M. K. Khan and M. A. Peters, Lipschitz constants for some approximation operators of a Lipschitz continuous function, J. Approx. Theory, 59 (1989) no. 3, pp. 307-315, http://dx.doi.org/10.1016/0021-9045(89)90096-8 DOI: https://doi.org/10.1016/0021-9045(89)90096-8

Zhongkai Li, Bernstein polynomials and modulus of continuity, J. Approx. Theory, 102 (2000) no. 1, pp. 171-174, http://dx.doi.org/10.1006/jath.1999.3374 DOI: https://doi.org/10.1006/jath.1999.3374

A. Lupaş, The approximation by some positive linear operators, In: Proceedings of the International Dortmund Meeting on Approximation Theory (M.W. Müller et al., eds.), Akademie Verlag, Berlin, (1995), pp. 201-229.

H. N. Mhaskar and D. V. Pai, Fundamentals of approximation theory, CRC Press, Boca Raton, FL; Narosa Publishing House, New Delhi, 2000.

S. Tarabie, On some A-statistical approximation processes, Int. J. Pure Appl. Math., 76 (2012) no. 3, pp. 327-332.

T. Trif, An elementary proof of the preservation of Lipschitz constants by the Meyer-König and Zeller operators, JIPAM. J. Inequal. Pure Appl. Math., 4 (2003) no. 5, Article 90, 3 pp.

Downloads

Published

2014-08-01

How to Cite

Erençin, A., Bașcanbaz-Tunca, G., & Tașdelen, F. (2014). Some properties of the operators defined by Lupaș. Rev. Anal. Numér. Théor. Approx., 43(2), 168–174. https://doi.org/10.33993/jnaat432-1027

Issue

Section

Articles