Generalized Krasnoselskii fixed point theorem involving auxiliary functions in bimetric spaces and application to two-point boundary value problem

In this paper, we introduce a generalized contraction of Krasnoselskii-type using auxiliary functions, and obtained some sufficient conditions for existence and uniqueness of fixed point for such mappings on bimetric spaces. We also establish a result on coincidence point of two mappings, and derive...

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Bibliographic Details
Published in:Applied mathematics and computation 2014-12, Vol.248, p.323-327
Main Authors: Berzig, Maher, Chandok, Sumit, Khan, Mohammad Saeed
Format: Article
Language:English
Subjects:
Bimetric space
Boundary value problems
Coincidence point
Computation
Differential equations
Fixed point
Fixed points (mathematics)
Mapping
Mathematical analysis
Mathematical models
Theorems
Two-point boundary value problem
Uniqueness
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Summary:In this paper, we introduce a generalized contraction of Krasnoselskii-type using auxiliary functions, and obtained some sufficient conditions for existence and uniqueness of fixed point for such mappings on bimetric spaces. We also establish a result on coincidence point of two mappings, and derive several corollaries of our main theorems. As application, we establish an existence result for a two-point boundary value problem of second order differential equation.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.09.096