WEIGHTED APPROXIMATION PROPERTIES OF GENERALIZED PICARD OPERATORS

Yilmaz B., Aral A., BAŞCANBAZ TUNCA G.

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, cilt.13, sa.3, ss.499-513, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 3
  • Basım Tarihi: 2011
  • Dergi Adı: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.499-513
  • Anahtar Kelimeler: Generalized Picard singular integral, Nonisotropic distance, Lebesgue point
  • Ankara Üniversitesi Adresli: Evet

Özet

In this work, we continue the study of generalized Picard operator P-lambda,P-beta ([2]) depending on nonisotropic beta-distance, in the direction of weighted approximation process. For this purpose, we first define weighted n-dimensional L-p space by involving weight depending on nonisotropic distance. Then we introduce a new weighted beta-Lebesgue point depending on nonisotropic distance and study pointwise approximation of P-lambda,P-beta to the unit operator at these points. Also, we compare the order of convergence at the weighted beta-Lebesgue point with the order of convergence of the operators to the unit operator. Finally, we show that this type of convergence also occurs with respect to nonisotropic weighted norm.