On a topological fuzzy fixed point theorem and its application to non-ejective fuzzy fractals. II. (English) Zbl 1423.54067
Summary: This paper deals mainly with new very general fuzzy fixed point theorems in metric spaces and their application to fuzzy fractals. It is a natural continuation of our paper [ibid. 350, 95–106 (2018; Zbl 1397.54046)] which significantly generalizes and improves the results by P. Diamond et al. [ibid. 86, No. 3, 377–380 (1997; Zbl 0917.54045)], where no application was given. Moreover, besides the existence, some further important properties of fixed point sets (in particular, fractals) like their weak local stability, called none-ejectivity in the sense of F. E. Browder [Duke Math. J. 32, 575–578 (1965; Zbl 0137.32601)], will be established.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54A40 | Fuzzy topology |
| 28A80 | Fractals |
Keywords:
fuzzy fixed points; fuzzy fractals; absolute retracts; multivalued maps; admissible maps; compact absorbing contractions; non-ejectivityReferences:
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