Abstract
AbstractWorking in the frame of variable bounded variation spaces in the sense of Wiener, introduced by Castillo, Merentes, and Rafeiro, we prove convergence in variable variation by means of the classical convolution integral operators. In the proposed approach, a crucial step is the convergence of the variable modulus of smoothness for absolutely continuous functions. Several preliminary properties of the variable $$p(\cdot )$$
p
(
·
)
-variation are also presented.
Funder
Università degli Studi di Perugia
Publisher
Springer Science and Business Media LLC