Geodesic
On the superposition operator in the space of functions of Hwq ([0, 1])
Filomat, Tome 37 (2023) no. 5, p. 1687

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DOI

In this paper, we obtained a necessary and sufficient condition for the embedding H ω q ([0, 1]) ⊂ IBV q p ([0, 1]), where IBV q p denotes the set of functions of bounded q-integral p-variation. Additionally, the conditions for the composition and superposition operators were provided to map the space H ω q ([0, 1]) into itself, by which these operators were bounded. Finally, we applied these results to examine the existence and uniqueness of solutions to Hammerstein integral equations in the space of H ω q ([0, 1]).
DOI : 10.2298/FIL2305687K
Classification : 47H30, 46A45
Keywords: Banach contraction principle, Composition operator, Hammerstein integral equation, Lipschitz condition, Modulus of continuity, Superposition operator, 1-periodic Function 
Sajjad Karami; Javad Fathi; Ahmad Ahmadi. On the superposition operator in the space of functions of Hwq ([0, 1]). Filomat, Tome 37 (2023) no. 5, p. 1687 . doi: 10.2298/FIL2305687K
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     title = {On the superposition operator in the space of functions of {Hwq} ([0, 1])},
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     year = {2023},
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     doi = {10.2298/FIL2305687K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2305687K/}
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