absolute retracts
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2021 ◽  
Vol 22 (1) ◽  
pp. 15-30
Author(s):  
Jan Andres ◽  
Jiřı́ Fišer ◽  
Lech Górniewicz

The existence of fixed points and, in particular, coupled fixed points is investigated for multivalued contractions in complete metric spaces. Multivalued coupled fractals are furthermore explored as coupled fixed points of certain induced operators in hyperspaces, i.e. as coupled compact subsets of the original spaces. The structure of fixed point sets is considered in terms of absolute retracts. We also formulate a continuation principle for multivalued contractions as a nonlinear alternative based on the topological essentiality. Two illustrative examples about coupled multivalued fractals are supplied.


2017 ◽  
Vol 12 (3) ◽  
pp. 535-549
Author(s):  
Ton Kloks ◽  
Yue-Li Wang
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2010 ◽  
Vol 310 (10-11) ◽  
pp. 1507-1519
Author(s):  
Cynthia Loten

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