IJPAM: Volume 77, No. 2 (2012)
SATISFYING LIPSCHITZ TYPE CONTRACTIVE CONDITION
Department of Pure and Applied Mathematics
Guru Ghasidas Vishwavidyalaya
Bilaspur (C. G.), INDIA
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 or 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