Convergence of sampling Kantorovich operators in modular spaces with applications

Abstract

Abstract In the present paper we study the so-called sampling Kantorovich operators in the very general setting of modular spaces. Here, modular convergence theorems are proved under suitable assumptions, together with a modular inequality for the above operators. Further, we study applications of such approximation results in several concrete cases, such as Musielak–Orlicz and Orlicz spaces. As a consequence of these results we obtain convergence theorems in the classical and weighted versions of the $$L^p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math> and Zygmund (or interpolation) spaces. At the end of the paper examples of kernels for the above operators are presented.

Locations

• Rendiconti del Circolo Matematico di Palermo Series 2 - View - PDF