Complete Asymptotic Expansions of Operators Related to Generalized Laguerre and Touchard Polynomials

ABSTRACT In this article, we provide complete asymptotic expansions of the linear positive operators associated with the generalized Laguerre and Touchard polynomials, respectively. We also provide specific methods to obtain better order of approximation by these operators. Moreover, we establish quantitative difference estimates for these operators with respect to their components through moduli of smoothness. Finally, we investigate their rates of convergence through graphical illustrations.