**Volume 10, Issue 10, pp 5132--5141**

**Publication Date**: 2017-10-12

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

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

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.

Homeomorphism metric space, multiplicative metric space, metric space, \(b\)-metric space, generalized contraction, fixed point, best proximity point

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