# On best proximity points for various $\alpha$-proximal contractions on metric-like spaces

Volume 9, Issue 8, pp 5202--5218 Publication Date: August 23, 2016

### Authors

Hassen Aydi - University of Dammam, Department of Mathematics, College of Education of Jubail, P. O. 12020, Industrial Jubail 31961, Saudi Arabia.
Abdelbasset Felhi - King Faisal University, Department of Mathematics, College of Sciences, Al-Hassa, Saudi Arabia.

### Abstract

We establish some best proximity points for various $\alpha$-proximal contractive non-self-mappings in the class of metric-like spaces. We provide concrete examples. We also present some best proximity point theorems in metric (metric-like) spaces endowed with a graph and in partially ordered metric spaces.

### Keywords

• Metric-like
• best proximity point
• fixed point
• controlled proximal contraction.

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