A new concept of fixed point in metric and normed interval spaces
type: Item
instance of: scholarly article
title: A new concept of fixed point in metric and normed interval spaces
zbMATH Open document ID: 1405.54032
author: Hsien-Chung Wu
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: The main aim of this paper is to propose the concept of so-called near fixed point and establish many types of near fixed point theorems in the set of all bounded and closed intervals in \(\mathbb R\). The concept of null set will be proposed in order to interpret the additive inverse element in the set of all bounded closed intervals. Based on the null set, the concepts of metric interval space and normed interval space are proposed, which are not the conventional metric and normed spaces. The concept of near fixed point is also defined based on the null set. In this case, we shall establish many types of near fixed point theorems in the metric and normed interval spaces.
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 6994822
zbMATH Keywords: metric interval space
zbMATH Keywords: normed interval space
zbMATH Keywords: near fixed point
zbMATH Keywords: null set
zbMATH Keywords: triangle inequality
MaRDI profile type: Publication
full work available at URL: math6110219
OpenAlex ID: W2898276214
cites work: Q3345690
cites work: Q3925093
cites work: Q5566070
cites work: Q3207999
cites work: Interval Methods for Systems of Equations
cites work: Hahn-Banach theorems in nonstandard normed interval spaces
cites work: Q4943597
cites work: Functional Analysis, Calculus of Variations and Optimal Control
cites work: Q3999065
cites work: A theorem on contraction mappings
Wikidata QID: Q129034654
DOI: 10.3390/MATH6110219
description: scientific article; zbMATH DE number 6994822