On generalizations of the Meir-Keeler type contraction maps
type: Item
instance of: scholarly article
title: On generalizations of the Meir-Keeler type contraction maps
zbMATH Open document ID: 0711.54028
DOI: 10.1016/0022-247X(90)90318-A
author: Sehie Park
author: Kwon Bai Moon
author: Billy E. Rhoades
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 4169651
zbMATH Keywords: generalized contractions
zbMATH Keywords: fixed point
zbMATH Keywords: Meir-Keeler type generalized contractive condition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4169651