On existence and uniqueness of \(g\)-best proximity points under \(\left(\varphi, \theta, \alpha, g\right)\)-contractivity conditions and consequences (Q1722381)
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scientific article; zbMATH DE number 7021960
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On existence and uniqueness of \(g\)-best proximity points under \(\left(\varphi, \theta, \alpha, g\right)\)-contractivity conditions and consequences |
scientific article; zbMATH DE number 7021960 |
Statements
On existence and uniqueness of \(g\)-best proximity points under \(\left(\varphi, \theta, \alpha, g\right)\)-contractivity conditions and consequences (English)
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14 February 2019
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Summary: We collect, improve, and generalize very recent results due to \textit{C. Mongkolkeha} et al. [ibid. 2014, Article ID 813614, 11 p. (2014; Zbl 1469.54159)] in three directions: firstly, we study \(g\)-best proximity points; secondly, we employ more general test functions than can be found in that paper, which lets us prove best proximity results using different kinds of control functions; thirdly, we introduce and handle a weak version of the \(P\)-property. Our results can also be applied to the study of coincidence points between two mappings as a particular case. As a consequence, the contractive condition we introduce is more general than was used in the mentioned paper.
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