REMARK ON WEIGHTED APPROXIMATION PROPERTIES OF GENERALIZED PICARD OPERATORS

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

MISKOLC MATHEMATICAL NOTES, vol.14, no.3, pp.1091-1103, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.18514/mmn.2013.574
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1091-1103
  • Keywords: generalized Picard singular integral nonisotropic distance, Lebesgue point
  • Ankara University Affiliated: Yes

Abstract

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.