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Fixed point theorems for expansion mappings satisfying implicit relations

Pathak H.K. (School of Studies in Mathematics, Pt. Ravishankar Shukla, University, Raipur, India)
Tiwari Rakesh (Department Of Mathematics, Govt.V.Y.T.PG. Autonomous, College, Durg, India)

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].

Keywords: common fixed points, expansion mappings, complete metric space, weak compatible mappings, implicit relations