Anastassiou, George A.Aral, Ali2020-06-252020-06-252009closedAccess0898-12211873-7668https://doi.org/10.1016/j.camwa.2008.09.026https://hdl.handle.net/20.500.12587/4491in this article, we introduce and study a new type of Picard singular integral operators on R-n constructed by means of the concept of the nonisotropic beta-distance and the q-exponential functions. The central role here is played by the concept of nonisotropic beta-distance, which allows one to improve and generalize the results given for classical Picard and q-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 beta-distance with respect to the uniform norm. Then we give the definition of beta-Lebesque points depending on nonisotropic beta-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. (C) 2008 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessPicard singular integralNonisotropic distanceq-exponentialRate of convergenceArticle57582183010.1016/j.camwa.2008.09.0262-s2.0-58749115562Q1WOS:000263708000014Q2