Integral Modification of Lupaş‐Type Operators for Improved Approximation and Reduced Bias

In this paper, we introduce a generalized class of Lupaş‐type operators constructed through an integral modification of the classical formulation. Instead of using discrete point evaluations, the proposed operators are defined by means of weighted local integral averages together with a parameter‐dependent structure. We investigate the approximation properties of the proposed operators by studying their moments and convergence behavior. In particular, a Korovkin‐type approximation theorem is established, and quantitative approximation estimates are obtained by means of the second modulus of smoothness and Peetre′s K ‐functional. The obtained results show that the integral modification reduces the bias of the classical construction and provides improved approximation behavior. Furthermore, the proposed operators preserve the convergence properties expected for positive linear operators on unbounded intervals.