Common best proximity results for multivalued proximal contractions in metric space with applications

The study of the best proximity points is an interesting topic of optimization theory. We introduce the notion of α*-proximal contractions for multivalued mappings on a complete metric space and establish the existence of common best proximity point for these mappings in the context of multivalued and single-valued mappings. As an application, we derive some best proximity point and fixed point results for multivalued and single-valued mappings on partially ordered metric spaces. Our results generalize and extend many known results in the literature. Some examples are provided to illustrate the results obtained herein.