Weighted approximation properties of generalized Picard operators

Abstract

In this work, we continue the study of generalized Picard operator P?,? ([2]) depending on nonisotropic ?-distance, in the direction of weighted approximation process. For this purpose, we first define weighted n-dimensional Lp space by involving weight depending on nonisotropic distance. Then we introduce a new weighted ?-Lebesgue point depending on nonisotropic distance and study pointwise approximation of ?,? to the unit operator at these points. Also, we compare the order of convergence at the weighted ?-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. © 2011 EUDOXUS PRESS, LLCAll rights reserved.