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Zbl 1133.54028
Zhang, Xian
Common fixed point theorems for some new generalized contractive type mappings. (English)
[J] J. Math. Anal. Appl. 333, No. 2, 780-786 (2007). ISSN 0022-247X

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.
[Dariusz Bugajewski (Baltimore)]

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: common fixed point theorem; generalized contractive; metric space

Cited in: Zbl 1248.54030 Zbl 1225.54015

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