Best Proximity Point for The Proinov Contraction

The theory of fixed-point points is naturally generalized to the context in which mappings are not self-maps, by the concept of best proximity points. The paper explores the presence and the uniqueness of best proximity points of Proinov-type contractions in metric spaces. A Proinov contraction is a generalization of classical contraction mappings, where there is a given inequality of the distance between image points and the corresponding domain elements. We do so by providing adequate conditions in which such contractions have best proximity points, and we have a single framework which contains known results in special cases. The contribution of our findings to the field of nonlinear analysis in general is to extend the use of fixed point techniques on non-self mappings, and we reinforce our theoretical findings with examples.