Convergence results in Orlicz spaces for sequences of max-product sampling Kantorovich operators (Q6572441)

In this paper, the authors provide some convergence properties of \textit{max-product sampling Kantorovich operators}, originally introduced in [\textit{L. Coroianu} et al., Anal. Appl., Singap. 19, No. 2, 219--244 (2021; Zbl 1464.41004)]. These operators are derived by modifying the definition of the sampling Kantorovich operators, replacing the series (or sum for finite terms) with the operator \(\bigvee\), which represents the supremum (or maximum, in the finite case) of a set of real numbers.\N\NIn particular, the authors establish, via density, a modular convergence theorem (Theorem 4.3) within the framework of Orlicz spaces \(L_{+}^{\varphi}(\Omega)\). In the proof, they examine both cases where \(\Omega = [a,b]\) or \(\Omega = \mathbb{R}\), together using suitable conditions on the kernel function. Such result extends the application of max-product sampling Kantorovich operators to a wide range of functional spaces, including also the case of not necessary continuous signals. The general setting of Orlicz spaces also enables the authors to deduce convergence results for several concrete cases, including Lebesgue spaces, Zygmund spaces, and spaces of exponential type.