ON APPROXIMATION PROPERTIES OF MODIFIED PICARD OPERATORS ON THE SEMI-REAL AXIS

Basar Yilmaz, Didem Aydın Arı

Abstract


In this paper, we dene and study the modifed Picard singular
integral operators which the domain of f is half line. we demonstrate uniform
convergence of Pn operators and determine the degree of this uniform con-
vergence as well and examined the asymptotic behavior of the operators by
proving a quantitative Voronovskaya theorem. Moreover, we study uniform
weighted approximation formula for the operators of Pn using a weighted Ko-
rovkin type theorem. Finally, given result regarding global smoothness preser-
vation properties for the operators of Pn.


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