Computational Analysis of Modified Baskakov Durrmeyer Operators: Local and Weighted Approximation

ABSTRACT In this paper, we present a Durrmeyer variant of the recently proposed Baskakov–Schurer–Stancu operators. The new operators use a Beta‐type integral kernel, which extends approximation capabilities for Lebesgue measurable functions. We start by establishing basic estimates and central moments, providing detailed proofs. Next, we use a weighted modulus of continuity to derive three theorems about the rate of convergence. Then, we prove three weighted approximation theorems through Korovkin‐type results in weighted spaces. Additionally, we establish a Voronovskaja‐type theorem with an asymptotic error estimate. The results show that the new operators maintain the flexibility of parameters while offering better smoothness and convergence rates. Finally, we include graphical examples to demonstrate the effectiveness, accuracy, and approximation behavior of the proposed operators.