Key result
Fixed point theorems for expansion mappings satisfying implicit relations were established, extending and improving previous mathematical results.
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New theorems relax completeness via alternative conditions; leaves open applied validation beyond theory.
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].
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Pathak et al. (2006) studied this question. Fixed point theorems for expansion mappings satisfying implicit relations were established, extending and improving previous mathematical results.
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