Max-Product Sampling Kantorovich Operators: Quantitative Estimates in Functional Spaces (Q6648808)

This paper investigates the approximation properties of max-product sampling Kantorovich operators, a nonlinear generalization of linear approximation operators introduced by Bede, Coroianu, and Gal. These operators, previously studied for Lp-spaces and spaces of continuous functions, replace linear sums with maximum or supremum calculations, achieving a superior order of approximation. The authors provide a quantitative modular estimate for the approximation error using Orlicz-type moduli of smoothness and K-functionals in the Orlicz setting, which includes Lp, interpolation, and exponential-type spaces as particular cases. The analysis covers both general and compact intervals, with a qualitative study of convergence rates for functions in suitable Lipschitz classes.