کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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472291 | 698701 | 2009 | 10 صفحه PDF | دانلود رایگان |
In this article, we introduce and study a new type of Picard singular integral operators on RnRn constructed by means of the concept of the nonisotropic ββ-distance and the qq-exponential functions. The central role here is played by the concept of nonisotropic ββ-distance, which allows one to improve and generalize the results given for classical Picard and qq-Picard singular integral operators. In order to obtain the rate of convergence we introduce a new type of modulus of continuity depending on the nonisotropic ββ-distance with respect to the uniform norm. Then we give the definition of ββ-Lebesque points depending on nonisotropic ββ-distance and a pointwise approximation result shown at these points. Furthermore, we study the global smoothness preservation property of these new type Picard singular integral operators and prove a sharp inequality.
Journal: Computers & Mathematics with Applications - Volume 57, Issue 5, March 2009, Pages 821–830