Fixed point theorem for expansion mappings of rational type on a implicit relation

AUTHOR AND
AFFILIATION

*A.S. SALUJA, **ALKESH KUMAR DHAKDE and ***DEVKRISHNA MAGARDE

KEYWORDS:

Common fixed points, expansion mappings, Complete metric space, weak compatible mappings , implicit relations

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ABSTRACT:

In this note a fixed point theorems on 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 extended and improve results of S.M. Kang2, M.A. Khan et al.3, B.E. Rhoades7 and T.Taniguchi8.

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In this note a fixed point theorems on 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 extended and improve results of S.M. Kang2, M.A. Khan et al.3, B.E. Rhoades7 and T.Taniguchi8.