IJPAM: Volume 77, No. 2 (2012)

COMMON FIXED POINT OF ABSORBING MAPPINGS
SATISFYING LIPSCHITZ TYPE CONTRACTIVE CONDITION

Urmila Mishra$^1$, R.P. Pathak$^2$, Rashmi$^3$
$^{1,3}$Department of Pure and Applied Mathematics
Guru Ghasidas Vishwavidyalaya
Bilaspur (C. G.), INDIA
$^2$Department of Mathematics
National Institute of Technology
Raipur (C.G.), INDIA


Abstract. In this paper we prove a common fixed point theorem considering a weaker contractive condition and using the new notion called absorbing map, replacing continuity of maps by weaker notion called reciprocal continuity and have used one pair of semi - compatible map instead of compatibility of sequence of mappings. Also we do not assume any condition either on $\delta$ or $\phi$ in our Lipschitz type contractive condition so our result establishes a fixed point theorems under a weaker condition than that of earlier result of [#!Pant2!#], [#!Pant3!#], [#!Pant4!#] and others.

Received: February 16, 2012

AMS Subject Classification: AMS 54H25, 47H10

Key Words and Phrases: common fixed point, absorbing maps, compatible maps, weak compatible maps, semi-compatible maps, reciprocal continuous

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 2