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

Kirk, W. A.; Srinivasan, P. S.; Veeramani, P.

Fixed Point Theory 4, No. 1, 79-89 (2003).

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.

Reviewer: Jarosław Górnicki (Rzeszów)

MSC:

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