Direct local and global approximation results for operators of Gamma type

ÖZARSLAN, M. Ali; KARSLI, HARUN

Direct local and global approximation results for operators of Gamma type

Harun KARSLI, (Abant İzzet Baysal Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Bolu, Türkiye)

M. Ali ÖZARSLAN (Doğu Akdeniz Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, KKTC)

Hacettepe Journal of Mathematics and Statistics

1 0

Yıl: 2010 Cilt: 39 Sayı: 2 Sayfa Aralığı: 241 - 253 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Direct local and global approximation results for operators of Gamma type

Öz:

In this paper some direct local and global approximation results are obtained for the modified Gamma operators defined by A. Izgi and B¨uy¨ukyazıcı (Approximation and rate of approximation on unbounded intervals, Kastamonu Edu. J. Okt. 11 (2), 451–460, 2003 (in Turkish)), and independently by H. Karsli (Rate of convergence of a new Gamma Type Operator for functions with derivatives of bounded vari- ation, Math. Comput. Modelling 45 (5-6), 617–624, 2007). Furthermore, a Voronoskaya type theorem is given for these operators.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Becker, M. Global approximation theorems for Sz´asz-Mirakyan and Baskakov operators in polynomial weight spaces, Indiana University Mathematics Journal 27 (1), 127–142, 1978.
[2] Chen, W. and Guo, S. On the rate of convergence of the Gamma Operator for functions of bounded variation, Approx. Theory Appl. 1 (5), 85–96, 1985.
[3] DeVore, R.A. and Lorentz, G.G. Constructive Approximation (Springer-Verlag, Berlin, 1993).
[4] Ditzian, Z. Direct estimate for Bernstein polynomials, J. Approx. Theory 79, 165–166, 1994.
[5] Duman, O. and ¨Ozarslan, M.A. Global approximation results for modified Szasz-Mirakjan operators, Taiwanese J. Math. (accepted).
[6] Felten, M. Local and global approximation theorems for positive linear operators, J. Approx. Theory 94, 396–419, 1998.
[7] Finta, Z. Direct local and global approximation theorems for some linear positive operators, Analysis in Theory and Applications 20 (4), 307–322, 2004.
[8] Izgi, A. Order of approximation of functions of two variables by a new type Gamma oper- ators, General Mathematics 17 (1), 23–32, 2009.
[9] Izgi, A. and B¨uy¨ukyazici, I. Approximation and rate of approximation on unbounded inter- vals, Kastamonu Edu. Journal Okt. 11 (2), 451–460, 2003 (in Turkish).
[10] Karsli, H. Rate of convergence of a new Gamma Type Operators for functions with deriva- tives of bounded variation, Math. Comput. Modelling 45 (5-6), 617–624, 2007.
[11] Karsli, H., Gupta, V. and Izgi, A. Rate of pointwise convergence of a new kind of gamma operators for functions of bounded variation, Appl. Math. Letters 22 (4), 505–510, 2009.
[12] Lupas, A. and M¨uller, M. Approximationseigenschaften der Gammaoperatoren, Math. Zeitschr. 98, 208–226, 1967.
[13] Mazhar, S.M. Approximation by positive operators on infinite intervals, Mathematica Balkanica 5 (2), 99–104, 1991.
[14] ¨Ozarslan, M.A. and Duman, O. Local approximation results for Szasz-Mirakjan type oper- ators, Arch. Math. (Basel) 90, 144–149, 2008.
[15] Swiderski, T. Global approximation theorems for the generalized modified Szasz- Mirakyan operators in polynomial weighted spaces, Demonstratio Math. 36 (2), 383–392, 2003.
[16] Totik, V. The Gamma operators in Lp spaces, Publ. Math. 32, 43–55, 1985.
[17] Xu, X. -W. and Wang, J.Y. Approximation properties of modified Gamma operators, J. Math. Anal. Appl. 332, 798–813, 2007.
[18] Zeng, X. -M. Approximation properties of gamma operators, J. Math. Anal. Appl. 311 (2), 389–401, 2005.

APA	KARSLI H, ÖZARSLAN M (2010). Direct local and global approximation results for operators of Gamma type. , 241 - 253.
Chicago	KARSLI HARUN,ÖZARSLAN M. Ali Direct local and global approximation results for operators of Gamma type. (2010): 241 - 253.
MLA	KARSLI HARUN,ÖZARSLAN M. Ali Direct local and global approximation results for operators of Gamma type. , 2010, ss.241 - 253.
AMA	KARSLI H,ÖZARSLAN M Direct local and global approximation results for operators of Gamma type. . 2010; 241 - 253.
Vancouver	KARSLI H,ÖZARSLAN M Direct local and global approximation results for operators of Gamma type. . 2010; 241 - 253.
IEEE	KARSLI H,ÖZARSLAN M "Direct local and global approximation results for operators of Gamma type." , ss.241 - 253, 2010.
ISNAD	KARSLI, HARUN - ÖZARSLAN, M. Ali. "Direct local and global approximation results for operators of Gamma type". (2010), 241-253.

APA	KARSLI H, ÖZARSLAN M (2010). Direct local and global approximation results for operators of Gamma type. Hacettepe Journal of Mathematics and Statistics, 39(2), 241 - 253.
Chicago	KARSLI HARUN,ÖZARSLAN M. Ali Direct local and global approximation results for operators of Gamma type. Hacettepe Journal of Mathematics and Statistics 39, no.2 (2010): 241 - 253.
MLA	KARSLI HARUN,ÖZARSLAN M. Ali Direct local and global approximation results for operators of Gamma type. Hacettepe Journal of Mathematics and Statistics, vol.39, no.2, 2010, ss.241 - 253.
AMA	KARSLI H,ÖZARSLAN M Direct local and global approximation results for operators of Gamma type. Hacettepe Journal of Mathematics and Statistics. 2010; 39(2): 241 - 253.
Vancouver	KARSLI H,ÖZARSLAN M Direct local and global approximation results for operators of Gamma type. Hacettepe Journal of Mathematics and Statistics. 2010; 39(2): 241 - 253.
IEEE	KARSLI H,ÖZARSLAN M "Direct local and global approximation results for operators of Gamma type." Hacettepe Journal of Mathematics and Statistics, 39, ss.241 - 253, 2010.
ISNAD	KARSLI, HARUN - ÖZARSLAN, M. Ali. "Direct local and global approximation results for operators of Gamma type". Hacettepe Journal of Mathematics and Statistics 39/2 (2010), 241-253.