REMARK ON WEIGHTED APPROXIMATION PROPERTIES OF GENERALIZED PICARD OPERATORS
MISKOLC MATHEMATICAL NOTES, cilt.14, sa.3, ss.1091-1103, 2013 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 3
- Basım Tarihi: 2013
- Doi Numarası: 10.18514/mmn.2013.574
- Dergi Adı: MISKOLC MATHEMATICAL NOTES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1091-1103
- Anahtar Kelimeler: generalized Picard singular integral nonisotropic distance, Lebesgue point
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Ankara Üniversitesi Adresli: Evet
Özet
In this article, we still hold the study of the generalized Picard operators P-lambda,P-beta (f; q) depending on nonisotropic beta-distance given in [3]. By continuing to deal with the nonisotropic weighted L-p,L-beta (R-n) space defined in [17], we introduce a new weighted L-p,L-beta modulus of continuity depending on the nonisotropic distance to obtain the weighted rate of convergence. We show that weighted convergence rate of P-lambda,P-beta (f; q) to f can be made better not only depending on the chosen q but also the choice of beta. We get that P-lambda,P-beta (f; q) satisfy the global smoothness preservation property via weighted L-p,L-beta modulus of continuity. Also we give direct approximation property of the generalized Picard operators P-lambda,P-beta (f; q) with respect to nonisotropic weighted norm.