Common fixed point theorems for some new generalized contractive type mappings. (English) Zbl 1133.54028

Zhang, Xian

J. Math. Anal. Appl. 333, No. 2, 780-786 (2007).

In this paper the author proves a common fixed point theorem for a pair of mappings \(T,\;S:X\to X\), where \((X,d)\) is a complete metric space, which satisfy a generalized contractive type condition: \[ F(d(Tx,Sy))\leq\psi(F(M(x,y))\quad\text{for all }\; x,y\in X, \] where \(M(x,y)=\max\{d(x,y),d(Tx,x), d(Sy,y),\frac{1}{2}(d(Tx,y)+d(Sy,x))\}\) and \(F\), \(\psi\) satisfy suitable assumptions. Some special cases and an example of a mapping which satisfies the above condition but does not satisfy the general contractive condition are also provided.

Reviewer: Dariusz Bugajewski (Baltimore)

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
47H10	Fixed-point theorems

Keywords:

common fixed point theorem; generalized contractive; metric space

References:

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