On an approximation processes in the space of analytical functions

• Autorzy: Akif Gadjiev , Arash Ghorbanalizadeh
• Języki publikacji: EN

Abstrakty

EN

In this paper we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on a bounded domain of the complex plane.

Słowa kluczowe

EN

The space of analytical functions; Conformal mapping; Linear k-positive operators; Korovkin type theorems

Kategorie tematyczne

• 41A36: Approximation by positive operators
• 41A25: Rate of convergence, degree of approximation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 2
• Strony: 389-398

Daty

wydano

2010-04-01

online

2010-04-14

Twórcy

autor

Akif Gadjiev

• Institute of Mathematics and Mechanics of NAS

autor

Arash Ghorbanalizadeh

• Institute of Mathematics and Mechanics of NAS

Bibliografia

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• [2] Altomare F., Campiti M., Korovkin-type approximation theory and its applications, In: de Gruyter Studies in Mathematics, Vol. 17, Walter de Gruyter and Co, Berlin, 1994
• [3] Duman O., Statistical approximation theorems by k-positive linear operators, Arch. Math., (Basel) 86, 2006, 6, 569–576
• [4] Evgrafov M.A., The method of near systems in the space of analytic functions and its application to interpolation, Trudy Moskov. Mat. Obsc., 1956, 5, 89–201 (in Russian)
• [5] Fast H., Sur la convergence statistique, Colloq. Math., 1951, 2, 241–244 (in French)
• [6] Gadjiev A.D., Linear k-positive operators in a space of regular functions, and theorems of P. P. Korovkin type, Izv. Akad. Nauk Azerbaidzan. SSR Ser. Fiz.-Tehn. Mat. Nauk, 1974, 5, 49–53 (in Russian)
• [7] Gadžiev A.D., A problem on the convergence of a sequence of positive linear operators on unbounded sets, and theorems that are analogous to P. P. Korovkin’s theorem, Dokl. Akad. Nauk SSSR, 218, 1974, 1001–1004 (in Russian)
• [8] Gadjiev A.D., Theorems of the type of P.P. Korovkin theorems, Mat. Zametki, 1976, 20, 781–786(in Russian)
• [9] Gadjiev A.D., Orhan C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 2002, 32, 129–138 http://dx.doi.org/10.1216/rmjm/1030539612
• [10] Hacisalihoglu H.H., Gadjiev A.D., On convergence of the sequences of linear positive operators, Ankara University Press, Ankara, 1995 (in Turkish)
• [11] İspir N., Convergence of sequences of k-positive linear operators in subspaces of the space of analytic functions, Hacet. Bull. Nat. Sci. Eng. Ser. B, 1999, 28, 47–53
• [12] İspir N., Atakut Ç., On the convergence of a sequence of positive linear operators on the space of m-multiple complex sequences, Hacet. Bull. Nat. Sci. Eng. Ser. B, 2000, 29, 47–54
• [13] Özarslan M.A., I-convergence theorems for a class of k-positive linear operators, Cent. Eur. J. Math., 2009, 7, 357–362 http://dx.doi.org/10.2478/s11533-009-0017-4

Identyfikatory

DOI

10.2478/s11533-010-0011-x