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Zbl 1052.54032
Kirk, W.A.; Srinivasan, P.S.; Veeramani, P.
Fixed points for mappings satisfying cyclical contractive conditions.
(English)
[J] Fixed Point Theory 4, No. 1, 79-89 (2003). ISSN 1583-5022

In the present paper the authors extend classical results due to Edelstein, Geraghty, Boyd and Wong, Caristi for mappings of the type $f:\bigcup^p_{i=1}A_i\to \bigcup^p_{i=1} A_i$, where $f(A_i)\subset A_{i+1}$, $i=1,\dots,p$ with $A_{p+1} = A_1$, where the contractive assumptions are restricted to pairs $(x,y)\in A_i\times A_{i+1}$. The paper concludes with a result about nonexpansive mappings in a Banach space setting.
[Jarosław Górnicki (Rzeszów)]
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

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