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

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.