Warianty tytułu
Języki publikacji
Abstrakty
In the present paper we introduce two q-analogous of the well known Baskakoy operators. For the first operator we obtain convergence property on bounded interval. Then we give the montonity on the sequence of q-Baskakov operators for n when the function f is convex. For second operator, we obtain direct approximation property on unbounded interval and estimate the rate of convergence. One can say that, depending on the selection of q, these operators are more flexible then the classical Baskakov operators while retaining their approximation properties.
Czasopismo
Rocznik
Tom
Strony
109-122
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
autor
- Faculty of Science and Arts Department of Mathematics Kirikkale University Yahihan, Kirikkale, Turkey, aral@science.ankara.edu.tr
Bibliografia
- [1] F. Altomare, M. Campiti, Korovkin-type Approximation Theory and its Applications, Vol. 17, de Gruyter Series Studies in Mathematics, de Gruyter, Berlin-New York, 1994.
- [2] F. Altomare, E. M. Mangino, On a generalization of Baskakov operator, Rev. Roumaine Math. Pures Appl. 44, 683-705.
- [3] G. E. Andrews, R. Askey, R. Roy, Special Functions, Cambridge Univ. Press, 1999.
- [4] A. Aral, A generalization of Szász-Mirakyan operators based on q-integers, Math. Comput. Modelling 47 (9-10) (2008), 1052-1062.
- [5] A. Aral, V. Gupta, q-derivative and applications to the q-Szász Mirakyan operators, Calcolo 43 (2006), 151-170.
- [6] V. A. Baskakov, An example of sequence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk. SSSR 113 (1957), 259-251.
- [7] F. Cao, C. Ding, Z. Xu, On multivariate Baskakov operator, J. Math. Anal. Appl. 307 (2005), 274-291.
- [8] E. W. Cheney, Introduction to Approximation Theory, Chelsea Pupishing Company. New York, 1982 (Second Edition).
- [9] T. Ernst, The history of q-calculus and a new method, U.U.D.M Report 2000, 16, ISSN 1101-3591, Department of Mathematics, Upsala University, 2000.
- [10] E. Ibikli, E. A. Gadjieva, The order of approximation some unbounded functions by the sequences of positive linear operators, Turkish J. Math. 19 (1995), 331-337.
- [11] S. Pethe, On the Baskakov operator, Indian J. Math. 26 (1984), No. 1-3, 43-48 (1985).
- [12] G. M. Phillips, Interpolation and Approximation by Polynomials, Springer-Verlag, 2003.
- [13] G. M. Phillips, On generalized Bernstein polynomials, in: D. F. Griffits, G. A. Watson (Eds.), Numerical Analysis: A. R. Mitchell 75th Birthday Volume, World Science, Singapore, 1996, pp. 263-269.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0051-0010