Approximation properties in abstract modular spaces for a class of general sampling-type operators

Abstract

In this article we study approximation properties for the class of general integral operators of the form

where G is a locally compact Hausdorff topological space, (H_w )_w>0 is a net of closed subsets of G with suitable properties and, for every w>0, μ _Hw is a regular measure on H_w We give pointwise, uniform and modular convergence theorems in abstract modular spaces and we apply the results to some kind of discrete operators including the sampling-type series.

Keywords:

• Modular approximation
• Nonlinear integral operators
• Regular families
• Singularity
• AMS Subject Classifications: 41A25
• 41A35
• 47G10
• 46E30