Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces

J Inequal Appl. 2018;2018(1):130. doi: 10.1186/s13660-018-1720-0. Epub 2018 Jun 11.


In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for this purpose. We define the best proximity points of such couplings that realize the distance between two sets. Our main theorem is deduced in metric spaces. As an application, we obtain the corresponding results in uniformly convex Banach spaces using the geometry of the space. We discuss two examples.

Keywords: Best proximity pair; Coupling; Metric spaces; Optimal approximate solution; Uniformly convex Banach space.