Korovkin type theorems for operators acting on functions of polynomial and exponential growth on $[0,\infty)$
Year: 2026
Type: preprint
Abstract: We establish two Korovkin-type approximation theorems for sequences of positive linear operators acting on continuous functions on $[0,\infty)$. The first result shows that pointwise convergence on all polynomial test functions implies pointwise convergence for every function in the domain that is dominated by a polynomial. The second result provides an analogous criterion for functions of exponential growth, where the test functions are the exponentials $e^{λx}$, $λ\in\mathbb{R}$. The results are applied to several classical and modified positive linear operators, including Baskakov, Szász--Mirakjan, Phillips, Post--Widder, Gamma, and Durrmeyer-type operators. Further applications are given to operators associated with modified Bessel functions and hyperbolic functions. The approach provides a unified framework for deriving pointwise convergence on unbounded intervals from convergence on suitable test functions.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166568041