Nemytskii Operator in Riesz-Bounded Variation Spaces with Variable Exponent

2016 ◽  
Vol 14 (1) ◽  
Author(s):  
René Erlín Castillo ◽  
Oscar Mauricio Guzmán ◽  
Humberto Rafeiro
Keyword(s):  
Bounded Variation ◽  
Variable Exponent ◽  
Nemytskii Operator

scholarly journals On the Nemytskii Operator in the Space of Functions of Bounded (p, 2, α)-Variation with Respect to the Weight Function

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Wadie Aziz
Keyword(s):  
Weight Function ◽  
Bounded Variation ◽  
The Other ◽  
Affine Function ◽  
Nemytskii Operator ◽  
Other Hand ◽  
Generator Function ◽  
Uniformly Continuous

AbstractIn this paper, we consider the Nemytskii operator (Hf)(t) = h(t, f(t)), generated by a given function h. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded (p,2,α)-variation (with respect to a weight function α) into the space of functions of bounded (q,2,α)-variation (with respect to α) 1<q<p, then H is of the form (Hf)(t) = A(t)f(t)+B(t). On the other hand, if 1<p<q then H is constant. It generalize several earlier results of this type due to Matkowski-Merentes and Merentes. Also, we will prove that if a uniformly continuous Nemytskii operator maps a space of bounded variation with weight function in the sense of Merentes into another space of the same type, its generator function is an affine function.

Nemytskii operator on $$(\phi ,2,\alpha )$$-bounded variation space in the sense of Riesz

2020 ◽  
Vol 11 (4) ◽  
pp. 2023-2043
Author(s):  
René E. Castillo ◽  
Edixon M. Rojas ◽  
Eduard Trousselot
Keyword(s):  
Bounded Variation ◽  
Nemytskii Operator

Corrigendum to “Variable exponent bounded variation spaces in the Riesz sense”

2020 ◽  
Vol 197 ◽  
pp. 111963
Author(s):  
René Erlín Castillo ◽  
Oscar Mauricio Guzmán ◽  
Humberto Rafeiro
Keyword(s):  
Bounded Variation ◽  
Variable Exponent

Variable exponent bounded variation spaces in the Riesz sense

2016 ◽  
Vol 132 ◽  
pp. 173-182 ◽  
Author(s):  
René E. Castillo ◽  
Oscar Mauricio Guzmán ◽  
Humberto Rafeiro
Keyword(s):  
Bounded Variation ◽  
Variable Exponent

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

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