# 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 language English 323-327 5 Applied Mathematics and Computation 248 https://doi.org/10.1016/j.amc.2014.09.096 Published - 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

In: Applied Mathematics and Computation, Vol. 248, 01.12.2014, p. 323-327.

Research output: Contribution to journalArticle

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