Existence of fixed points for Θ-type contraction and Θ-type Suzuki contraction in complete metric spaces

Fixexd point theory and applications

Shih-sen Chang¹  Xin-dong Liu²  Liang Cai Zhao²  Yun Xiao² 

[1] Center for General Education, China Medical University, Taichung, Taiwan;Institute of Mathematics, Yibin University, Yibin, China

关键词: Banach contraction principle;    fixed point;    Θ-type contraction;    Θ-type Suzuki contraction;    47H09;    49M05;    47H10;   

DOI  :  10.1186/s13663-016-0496-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to introduce the notions of Θ-type contractions and Θ-type Suzuki contractions and to establish some new fixed point theorems for these two kinds of mappings in the setting of complete metric spaces. The results presented in the paper are an extension of the Banach contraction principle, the Suzuki contraction theorem, and the Jleli and Samet fixed point theorem. As an application, we utilize our results to study the existence problem of solutions of nonlinear Hammerstein integral equations.

【 授权许可】

CC BY