What does this research mean for the field?

A newly proposed sequence of integral operators combining modified Laguerre polynomials and Păltănea basis functions successfully approximates functions over the interval [0, ∞) with mathematically proven convergence properties and asymptotic behavior. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to establish new operators for function approximation using modified Laguerre polynomials.

June 1, 2026Open Access

Approximation by a new sequence of operators involving Laguerre polynomials

Puntos clave

The aim is to establish new operators for function approximation using modified Laguerre polynomials.
Developed an integral approach with modified Laguerre polynomials and Păltănea basis function.
Conducted convergence analysis using Lipschitz class, Peetre's K-functional, and other methods.
Utilized numerical examples in Mathematica to verify theoretical results.
Established universal Korovkin's theorem for the proposed operators.
Derived Voronovskaja-type asymptotic formula related to the approximation properties.
Obtained significant approximation results in weighted spaces.

Resumen

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.

Preguntar a la IA

Me gusta

Guardar

Ver artículo completo