Best proximity points: Convergence and existence theorems for p-cyclic mappings

Abstract

We introduce a new class of mappings, called p-cyclic \phi-contractions, which contains the p-cyclic contraction mappings as a subclass. Then, convergence and existence results of best proximity points for p-cyclic \phi-contraction mappings are obtained. Moreover, we prove results of the existence of best proximity points in a reflexive Banach space. These results are generalizations of the results of Al-Thagafi and Shahzad (2009) [8].