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Some \(g\)-best proximity point results in \(G\)-metric spaces. (English) Zbl 1350.54035

Summary: The notions of \(G\)-generalized proximal contraction mappings of first and second kinds with respect to a mapping \(g\) in a \(G\)-metric space are introduced and some \(g\)-best proximity point theorems for such kind of nonself mappings in this space are established. Moreover, some examples to support the results proved herein are presented. To the best of our knowledge, no results are known at the moment for this kind of mappings in \(G\)-metric spaces. Our results even without the mapping \(g\) are new. Some results in the existing literature are also generalized by our results.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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