NONCYCLIC φ-CONTRACTIONS IN HYPERBOLIC UNIFORMLY CONVEX METRIC SPACES.

This paper aims to study the convergence of Picard's iteration to a best proximity pair for a class of noncyclic mappings with the help of projections in hyperbolic uniformly convex metric spaces. Some sufficient conditions are provided to guarantee the existence of a common best proximity pair for a pair of noncyclic mappings. Moreover, the existence and convergence of best proximity pairs for asymptotic pointwise noncyclic orbital contractions is studied. The main conclusions are supported with illustrative examples. [ABSTRACT FROM AUTHOR]