Abstract In this paper, we investigate the existence of best proximity points for classes of multivalued mappings that are not necessarily self mappings, defined on a pair of subsets in strictly convex and reflexive Banach spaces. A fixed point framework based on the Himmelberg fixed point theorem is used to derive the existence of best proximity point in the absence of self-mapping properties. Several examples are provided to illustrate the applicability of our results. The work contributes to the development of best proximity theory for multivalued nonlinear operators in Banach spaces and enriches the existing literature on approximation of fixed points through nearest point relations.
Upadhyay et al. (Tue,) studied this question.