Approximation by a new sequence of operators involving Laguerre polynomials

Abstract

This paper presents a new integral approach for operators using the modified Laguerre polynomials and P\u{a}lt\u{a}nea basis function to approximate functions over the interval $[0,\infty)$. Further, the universal Korovkin's theorem is established to investigate the approximation properties of the proposed operators. Convergence analysis is examined through various analytical methods, including the Lipschitz class, Peetre's $K$-functional, the second-order modulus of smoothness, and the modulus of continuity. The Voronovskaja-type asymptotic formula and approximation results in weighted spaces are also obtained. Finally, we employ Mathematica software to demonstrate numerical examples to validate the visual representation of the theoretical findings.