Extended Φ-contraction mappings

We extend the concept of Φ-contraction mappings and introduce a condition that applies to contraction mappings as well as nonexpansive mappings. The fixed-point sets and domains of such mappings display interesting algebraic, geometric and dynamical features. A method for determining the cardinality of the fixed-point set is also given. Various examples and an application in obtaining a unique solution of a boundary value problem of second order differential equations substantiate our results.