Fixed point theorems for expansion mappings satisfying implicit relations

Abstract

In this note a fixed point theorem for expansion mappings is established in a complete metric space under certain conditions. Further a common fixed point theorem for pair of weakly compatible expansion mappings is established. In this theorem the completeness of space is replaced with a set of four alternative conditions for functions satisfying implicit relations. These theorems extend and improve results of S. M. Kang [4], M. A. Khan et al. [5] B. E. Rhoades [11] and T. Taniguchi [12].