On generalized weakly directional contractions and approximate fixed point property with applications

Fixexd point theory and applications

Wei-Shih Du¹ 

[1] Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, Taiwan

关键词: τ-function;    τ0-metric;    Reich's condition;    directional hidden contraction;    approximate fixed point property;    generalized Mizoguchi-Takahashi's fixed point theorem;    generalized Berinde-Berinde's fixed point theorem;   

DOI  :  10.1186/1687-1812-2012-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we first introduce the concept of directional hidden contractions in metric spaces. The existences of generalized approximate fixed point property for various types of nonlinear contractive maps are also given. From these results, we present some new fixed point theorems for directional hidden contractions which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem and some well-known results in the literature. MSC: 47H10; 54H25.

【 授权许可】

CC BY