Fixed point theorems for alpha-contractive mappings of Meir–Keeler type and applications
Articles
Maher Berzig
Tunis College of Sciences and Techniques, Tunisia
Mircea-Dan Rus
Technical University of Cluj-Napoca, Romania
Published 2014-04-10
https://doi.org/10.15388/NA.2014.2.3
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Keywords

fixed point
α-contractive mapping of Meir–Keeler type
coupled fixed point
cyclic contraction
ordered metric space
two point boundary value problem

How to Cite

Berzig M. and Rus M.-D. (2014) “Fixed point theorems for alpha-contractive mappings of Meir–Keeler type and applications”, Nonlinear Analysis: Modelling and Control, 19(2), pp. 178-198. doi: 10.15388/NA.2014.2.3.

Abstract

In this paper, we introduce the notion of α-contractive mapping of Meir–Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this type of contraction. The presented theorems extend, generalize and improve several existing results in literature. To validate our results, we establish the existence and uniqueness of solution to a class of third order two point boundary value problems.

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