We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.
"Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space." J. Appl. Math. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/150941