Approximation by a new sequence of operators involving Laguerre polynomials

Thispaper presents a new integral approach for operators using the modified Laguerre polyno-mials and Păltă nea basis function to approximate functions over the interval [0, ∞). Further, the universal Korovkin’s theorem is established to investigate the approximation properties of the proposed opera-tors. 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 to present numerical examples that visually confirm the theoretical results.