Fixed point theorems for alpha-contractive mappings of Meir–Keeler type and applications

Nonlinear Analysis

Mircea-Dan Rus¹  Maher Berzig² 

[1] Technical University of Cluj-Napoca, Romania;Tunis College of Sciences and Techniques, Tunisia;

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

DOI  :  10.15388/NA.2014.2.3

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown