Common fixed point theorems of Gregus type for weakly compatible mappings satisfying generalized contractive conditions
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Date
2008
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Abstract
We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in
metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed
points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007
(2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10
(2003) 369–378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying
contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31–45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj,
A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15
(2005) 2359–2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal.
Appl. 333 (2) (2007) 780–786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.K. Pathak,
M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl.
53 (2007) 961–971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property
(E.A) and a common property (E.A).
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Keywords
Weakly compatible mappings, Common fixed point, Metric space, Generalized contractive condition