Feng–Liu type approach to best proximity point results for multivalued mappings

Let ( X , d ) be a metric space, A and B be two nonempty subsets of X , and T : A → B be a mapping. In this case, since the equation x = T x may not have an exact solution, it is meaningful to explore the approximate solution. The best approximation results in the literature are related to investigate such solutions. Further, best proximity point theorems not only investigate the approximate solution of the equation x = T x , but also an optimal solution of the minimization problem min { d ( x , T x ) : x ∈ A } . Such points are called the best proximity points of the mapping T . In this paper, considering the Feng and Liu’s approach in fixed point theory, we present some new results for best proximity points of nonself multivalued mappings.