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

We introduce a new class of mappings, called pp-cyclic φφ-contractions, which contains thepp-cyclic contraction mappings as a subclass. Then, convergence and existence results of best proximity points for pp-cyclic φφ-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].