Fixed points for mappings satisfying cyclical contractive conditions. (English) Zbl 1052.54032

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.


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