What question did this study set out to answer?

This research aims to define and analyze modified Picard singular integral operators on the half-plane, focusing on their convergence and approximation properties.

May 19, 2026Filomat0 citationsOpen Access

On the modification of Picard operators on the semi-real axis

BYBaşar Yılmaz ADAydin Didem

Key Points

This research aims to define and analyze modified Picard singular integral operators on the half-plane, focusing on their convergence and approximation properties.
Defined modified Picard singular integral operators on the half-plane.
Demonstrated uniform convergence and analyzed asymptotic behavior using a Voronovskaya theorem.
Studied uniform weighted approximations through a Korovkin type theorem.
Demonstrated uniform convergence of P_n^* operators.
Established results on global smoothness preservation for P_n^* operators.
Provided a quantitative Voronovskaya theorem confirming asymptotic behavior.

Abstract

In this paper, we define and study the modified Picard singular integral operators on the half plane. We demonstrate uniform convergence of Pₙ^* operators, determine the degree of this uniform convergence as well and examine the asymptotic behavior of the operators by proving a quantitative Voronovskaya theorem. Moreover, we study uniform weighted approximation formula for the operators of Pₙ^* by using a weighted Korovkin type theorem. Finally, we give a result regarding global smoothness preservation properties for the operators of Pₙ^*.

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