Remark on weighted approximation properties of generalized Picard operators

B. Yilmaz, G. Başcanbaz Tunca, A. Aral
2013 Miskolc Mathematical Notes  
In this article, we still hold the study of the generalized Picard operators P ;ˇ. f I q/ depending on nonisotropicˇ distance given in [3] . By continuing to deal with the nonisotropic weighted L p;ˇ. R n / space defined in [17], we introduce a new weighted L p;ˇm odulus of continuity depending on the nonisotropic distance to obtain the weighted rate of convergence. We show that weighted convergence rate of P ;ˇ. f I q/ to f can be made better not only depending on the chosen q but also the
more » ... q but also the choice ofˇ: We get that P ;ˇ. f I q/ satisfy the global smoothness preservation property via weighted L p;ˇm odulus of continuity. Also we give direct approximation property of the generalized Picard operators P ;ˇ. f I q/ with respect to nonisotropic weighted norm.
doi:10.18514/mmn.2013.574 fatcat:fx3kdbvdmnft3ab2ajakwekizq