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

Maher Berzig, Sumit Chandok, Mohammad Saeed Khan

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)323-327
Number of pages5
JournalApplied Mathematics and Computation
Volume248
DOIs
Publication statusPublished - Dec 1 2014

Fingerprint

Krasnoselskii's Fixed Point Theorem
Auxiliary Function
Two-point Boundary Value Problem
Boundary value problems
Generalized Contraction
Coincidence Point
Second order differential equation
Existence Results
Corollary
Existence and Uniqueness
Differential equations
Fixed point
Sufficient Conditions
Theorem

Keywords

  • Bimetric space
  • Coincidence point
  • Fixed point
  • Two-point boundary value problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

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AU - Khan, Mohammad Saeed

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AB - 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.

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KW - Coincidence point

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KW - Two-point boundary value problem

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