Studies modified Picard operators' convergence and behavior in a defined mathematical space, suggesting important implications for approximation theory.
In this paper, we define and study the modified Picard singular integral operators on the half plane. We demonstrate uniform convergence of P_n^* 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 P_n^* by using a weighted Korovkin type theorem. Finally, we give a result regarding global smoothness preservation properties for the operators of P_n^* .
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Yılmaz et al. (2025) studied this question.
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