## Fixed points for four mappings.(English)Zbl 0767.54037

Let $$A$$, $$B$$, $$S$$, $$T$$ be selfmappings of a complete metric space $$(X,d)$$ such that at least one of them is continuous; $$A$$, $$B$$ are surjective; the pairs $$A$$, $$S$$ and $$B$$, $$T$$ are compatible in the sense of Jungck; and $$\phi(d(Ax,By))\geq d(Sx,Ty)$$, $$x,y\in X$$, where $$\phi: [0,\infty)\to [0,\infty)$$ is non-decreasing, upper-semicontinuous and $$\phi(t)<t$$ $$(t>0)$$. Under these assumptions the authors prove that $$A$$, $$B$$, $$T$$, $$S$$ have a unique common fixed point. This is a generalization of an earlier result of the second author. Some examples show that surjectivity and compatibility conditions are necessary.

### MSC:

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