Geodesic
Self similarity sets via fixed point theory with lack of convexity
Filomat, Tome 37 (2023) no. 29, p. 10055

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DOI

A well-known theorem of fractal geometry, presented by J. Hutchinson ([16]), says that there exists a unique compact self similar set with respect to any finite set of contractions on a complete metric space. Motivated by this result, in this paper, we prove fixed set theoretical theorems in order to obtain useful variations of this important result for Meir-Keeler operators and using the technique of measure of weak-noncompactness for operators acting in Banach spaces and Banach algebras.
DOI : 10.2298/FIL2329055A
Classification : 47H09, 47H10, 47H30
Keywords: Krasnosel’skii theorem, Fixed set, Weak topology, Self-similarity theory 
Sana Hadj Amor; Ameni Remadi. Self similarity sets via fixed point theory with lack of convexity. Filomat, Tome 37 (2023) no. 29, p. 10055 . doi: 10.2298/FIL2329055A
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     author = {Sana Hadj Amor and Ameni Remadi},
     title = {Self similarity sets via fixed point theory with lack of convexity},
     journal = {Filomat},
     pages = {10055 },
     year = {2023},
     volume = {37},
     number = {29},
     doi = {10.2298/FIL2329055A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2329055A/}
}
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