Approximation by a new positive linear operator with exponential weight function

A new class of positive linear operators is constructed by incorporating an exponential weight function with the aim of enhancing approximation performance. The convergence behavior of the proposed operators is examined using Korovkin’s theorem, and a Voronovskaja-type asymptotic formula is derived to assess the convergence rate. Comparative numerical experiments with classical operators, including Baskakov and Bernstein operators, are conducted. The results indicate that the proposed operators provide significantly improved approximation accuracy over a wider range of test functions.