We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results.
Nashine, H.K., Kumam, P., Vetro, C. (2013). Best proximity point theorems for rational proximal contractions. FIXED POINT THEORY AND APPLICATIONS, 2013, 1-11 [10.1186/1687-1812-2013-95].
Best proximity point theorems for rational proximal contractions
VETRO, Calogero
2013-01-01
Abstract
We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results.
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