Fixed point problem of a multi-valued Kannan-Geraghty type contraction via \(w\)-distance. (English) Zbl 1507.54020
Summary: Combining certain existing concepts we define a new multi-valued contraction with respect to \(w\)-distance. The underline metric space is assumed to have a relation defined on it. We prove the existence of non-null fixed point sets for these mappings under appropriate assumptions. The uniqueness of the fixed point is proved separately under some additional conditions. We also discuss Hyers-Ulam-Rassias stability and well-posedness property of the fixed point problem. For that purpose we formulate them here in terms of \(w\)-distance. There are several corollaries, illustrative examples and remarks. Some existing results are shown to be extended by our result. The study is in the domain of multi-valued relational fixed point theory with \(w\)-distance.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
\(w\)-distance; Kannan contraction; Geraghty-type mapping; Hyers-Ulam-Rassias stability; well-posednessReferences:
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