First we introduce new concepts of contraction mappings, then we establish certain best proximity point theorems for such kind of mappings in metric spaces. Finally, as consequences of these results, we deduce best proximity point theorems in metric spaces endowed with a graph and in partially ordered metric spaces. Moreover, we present an example and some fixed point results to illustrate the usability of the obtained theorems.
Kumam, P., Salimi, P., Vetro, C. (2014). Best proximity point results for modified α-proximal C-contraction mappings. FIXED POINT THEORY AND APPLICATIONS, 2014, 1-16 [10.1186/1687-1812-2014-99].
Best proximity point results for modified α-proximal C-contraction mappings
VETRO, Calogero
2014-01-01
Abstract
First we introduce new concepts of contraction mappings, then we establish certain best proximity point theorems for such kind of mappings in metric spaces. Finally, as consequences of these results, we deduce best proximity point theorems in metric spaces endowed with a graph and in partially ordered metric spaces. Moreover, we present an example and some fixed point results to illustrate the usability of the obtained theorems.
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