Fixed point theorems for compatible multi-valued and single-valued mappings
type: Item
instance of: scholarly article
title: Fixed point theorems for compatible multi-valued and single-valued mappings
zbMATH Open document ID: 0671.54023
DOI: 10.1155/S0161171289000293
author: Hideaki Kaneko
author: Salvatore Sessa
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46365
review text: \textit{G. Jungck} [Am. Math. Mon. 83, 261-263 (1976; Zbl 0321.54023)] proved that if f: \(X\to X\) is a continuous map of a complete metric space (X,d) and g: \(X\to X\) a map which commutes with f, and if g(X)\(\subset f(X)\) and d(gx,gy)\(\leq hd(fx,fy)\) for all \(x,y\in X\) and some \(0\leq h\leq 1\), then f and g have a unique common fixed point. The authors obtain extensions of this theorem by replacing single-valued mappings with multi-valued ones, and commutativity with an adaptation of the weak commutativity of the second author [Publ. Inst. Math., Nouv. Sér. 32(46), 146-153 (1982; Zbl 0523.54030)] to the multi-valued setting. The definitions and results are too long to state here.
reviewed by: Helga Schirmer
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 4098281
zbMATH Keywords: complete metric space
zbMATH Keywords: weak commutativity
MaRDI profile type: Publication
OpenAlex ID: W1989490534
description: scientific article; zbMATH DE number 4098281