2024/11/23 by Danilo Costarellı, Costarelli, Danilo, Mariarosaria Natale +1 · 2 citations
Physics and Astronomy · #FOS: Mathematics #Functional Analysis (math.FA) #Optical and Acousto-Optic Technologies
paper · pdf · doi:10.48550/arxiv.2411.15475
openalex publication_date 2024/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the nonlinear exponential Kantorovich sampling series. We establish pointwise and uniform convergence properties and a nonlinear asymptotic formula of the Voronovskaja-type given in terms of the limsup. Furthermore, we extend these convergence results to Mellin-Orlicz spaces with respect to the logarithmic (Haar) measure. Quantitative results are also given, using the log-modulus of continuity and the log-modulus of smoothness, respectively, for log-uniformly continuous functions and for functions in Mellin-Orlicz spaces. Consequently, the qualitative order of convergence can be obtained in case of functions belonging to suitable Lipschitz (log-Hölderian) classes.