In this study, we analyze the approximation characteristics of the operators based on Laguerre polynomials. Initially, we present moments and central moments followed by certain results viz. asymptotic formula and difference estimates. Furthermore, we modify these operators to preserve linear functions and we prove that our modified operators have a finer error estimate than the original operators. Also, we demonstrate the convergence of both the operators with graphical illustrations.
Agrawal et al. (Wed,) studied this question.