Open Access Research

Periodic points for the weak contraction mappings in complete generalized metric spaces

Chi-Ming Chen1* and Chao-Hung Chen2

Author Affiliations

1 Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan

2 Department of Applied Mathematics, Chung Yuan Christian University, Chungli City, Taiwan

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Fixed Point Theory and Applications 2012, 2012:79 doi:10.1186/1687-1812-2012-79

Published: 9 May 2012

Abstract

In this article, we introduce the notions of (ϕ - φ)-weak contraction mappings and (ψ - φ)-weak contraction mappings in complete generalized metric spaces and prove two theorems which assure the existence of a periodic point for these two types of weak contraction.

Mathematical Subject Classification: 47H10; 54C60; 54H25; 55M20.

Keywords:
Periodic point; Meir-Keeler function; (ϕ - φ)-weak contraction mapping; (ψ - φ)-weak contraction mapping