Weak P-property on product spaces and related multidimensional best proximity point theorems

Abstract

In recent times, many authors proved several coupled, tripled, quadrupled and, in general, multidimensional fixed point theorems. In many cases, these results become to be simple consequences of their corresponding unidimensional theorems. In this paper, we show how the weak P-property can be induced in product spaces and how to use it to enunciate some kind of multidimensional (including coupled and tripled) best proximity (and fixed) point theorems.