On generalizations of the Meir-Keeler type contraction maps
The main result of the paper is a generalization of a fixed point theorem due to Meir and Keeler for mappings defined on complete metric spaces. The authors also include a survey showing that their result includes over 50 others appearing in the literature. The result is very technical. The Meir-Keeler condition is extended to a sequence of (not necessarily continuous) mappings pairwise satisfying a Meir-Keeler type generalized contractive condition, and various weak commutativity conditions are assumed to hold between mappings of the sequence and two `special' mappings. Certain restrictions on the ranges of these mappings are also assumed. The conclusion is that all mappings involved have a unique common fixed point.
Meir-Keeler type generalized contractive condition
scientific article; zbMATH DE number 4169651
scientific article