Convergence of Perturbed Sampling Kantorovich Operators in Modular Spaces
RESULTS IN MATHEMATICS(2023)
摘要
In the present paper we study the perturbed sampling Kantorovich operators in the general context of the modular spaces. After proving a convergence result for continuous functions with compact support, by using both a modular inequality and a density approach, we establish the main result of modular convergence for these operators. Further, we show several instances of modular spaces in which these results can be applied. In particular, we show some applications in Musielak–Orlicz spaces and in Orlicz spaces and we also consider the case of a modular functional that does not have an integral representation generating a space, which can not be reduced to previous mentioned ones.
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关键词
Perturbed sampling Kantorovich operators,modular spaces,modular convergence,uniform convergence,Musielak–Orlicz and Orlicz spaces
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