# Homeomorphism metric space and the fixed point theorems

Volume 10, Issue 10, pp 5132--5141

Publication Date: 2017-10-12

http://dx.doi.org/10.22436/jnsa.010.10.01

### Authors

Yinglin Luo - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
Yongfu Su - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
Wenbiao Gao - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

### Abstract

The purpose of this paper is to introduce the concept of the homeomorphism metric space and to prove the fixed point theorems and the best proximity point theorems for generalized contractions in such spaces. The multiplicative metric space is a special form of the homeomorphism metric space. The results of this paper improve and extend the previously known ones in the literature.

### Keywords

Homeomorphism metric space, multiplicative metric space, metric space, $b$-metric space, generalized contraction, fixed point, best proximity point