On characterizations of fixed and common fixed points
type: Item
instance of: scholarly article
title: On characterizations of fixed and common fixed points
zbMATH Open document ID: 0907.54038
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-29T00:00:00Z
review text: The authors introduce the concept of \(L\)-mapping which is equivalent to the concept of \(C\)-mapping introduced by \textit{S. Zhang} [Proc. Am. Math. Soc. 97, 343-346 (1986; Zbl 0593.54045)] and establish criteria for the existence of fixed points of \(L\)-mappings. By using the ideas of Jungck and Dien, the authors also obtain some necessary and sufficient conditions for the existence of fixed and common fixed points of continuous mappings. The results presented in this paper generalize, improve and unify the corresponding results of \textit{S. Zhang} [loc. cit.], \textit{Nguyen Huu Dien} [J. Math. Anal. Appl. 187, No. 1, 76-90 (1994; Zbl 0810.54034)], \textit{B. Fisher} [Math. Semin. Notes, Kobe Univ. 7, 81-84 (1979; Zbl 0415.54030)] and \textit{G. Jungck} [Am. Math. Mon. 83, 261-263 (1976; Zbl 0321.54025)].
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1218615
zbMATH Keywords: common fixed point
zbMATH Keywords: period point
zbMATH Keywords: compatible mapping
zbMATH Keywords: \(C\)-mapping
zbMATH Keywords: \(L\)-mapping
author: Zeqing Liu
author: Yuguang Xu
author: Yeol Je Cho
reviewed by: Shihsen Chang
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5947
OpenAlex ID: W2092566582
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DOI: 10.1006/JMAA.1998.5947
description: scientific article; zbMATH DE number 1218615