α-φ Contractions in Fractal Spaces

Abstract

The aim of this work is to introduce -admissible mapping in fractal spaces and prove fixed point theorem in the metric space of fractals. To establish the theorem we use    contraction condition on -admissible mapping. Here we consider the underlying metric space  is complete metric space and by using previous knowledge the fractal space on this underlying space  is also complete metric space. This completeness property of fractal space yields the existence of fixed point of invariant mapping defined on fractal space.  To clarify the convergence of fractals we introduce matrix of convergent sequences of contractions.