Degree of Approximation for Nonlinear Multivariate Sampling Kantorovich Operators on Some Functions Spaces

Abstract

In this article, the problem of the order of approximation for the nonlinear multivariate sampling Kantorovich operators is investigated. The case of uniformly continuous and bounded functions belonging to Lipschitz classes is considered, as well as the case of functions in Orlicz spaces. In the latter setting, suitable Zygmung-type classes are introduced by using the modular functionals of the spaces. The results obtained show that the order of approximation depends on both the kernels of our operators and the engaged functions. Several examples of kernels are considered in special instances of Orlicz spaces, typically used in approximation theory and for applications to signal and image processing.

Keywords:

• Irregular sampling
• Lipschitz classes
• Nonlinear multivariate sampling Kantorovich operators
• Order of approximation
• Orlicz spaces

Mathematics Subject Classification:

• 41A25
• 41A30
• 46E30
• 47A58
• 47B38
• 94A12