A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations

The aim of this paper is to extend the results of Harjani and Sadarangani and some other authors and to prove a new fixed point theorem of a contraction mapping in a complete metric space endowed with a partial order by using altering distance functions. Our theorem can be used to investigate a larg...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2012; no. 1; pp. 1 - 13
Main Authors: Yan, Fangfang, Su, Yongfu, Feng, Qiansheng
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 18.09.2012
Springer Nature B.V
Subjects:
Analysis
Applications of Mathematics
Boundary value problems
Differential equations
Differential Geometry
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Metric space
Nonlinearity
Theorems
Topology
altering distance function
partially ordered metric spaces
differential equation
contraction mapping principle
fixed point
ISSN:1687-1812, 1687-1820, 1687-1812, 2730-5422
Online Access:Get full text
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Summary:The aim of this paper is to extend the results of Harjani and Sadarangani and some other authors and to prove a new fixed point theorem of a contraction mapping in a complete metric space endowed with a partial order by using altering distance functions. Our theorem can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence of a solution for a periodic boundary value problem.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:1687-1812
1687-1820
1687-1812
2730-5422
DOI:10.1186/1687-1812-2012-152