Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions

Abstract

The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of b−metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness of b−metric spaces via the existence of best proximity points of non-self quasi-contractions. Further, we pose some questions related to the findings in the paper. An example is provided to illustrate the main result. The results obtained herein improve some well known results in the literature.

Keywords

• completeness
• quasi-contraction
• best proximity points
• <i>b</i>−metric
• non-self mappings