Homeomorphism metric space and the fixed point theorems
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
References
[1] R. P. Agarwal, E. KarapÄ±nar, B. Samet, An essential remark on fixed point results on multiplicative metric spaces, Fixed Point Theory Appl., 2016 (2016), 3 pages.
[2] A. E. Bashirov, E. M. Kurplnar, A. Ozyaplcl, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36–48.
[3] A. E. Bashirov, E. Misirli, Y. Tandogdu, A. Ozyaplcl, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ., 26 (2011), 425–438.
[4] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5–11.
[5] K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 112 (1969), 234–240.
[6] L. Florack, H. Van Assen, Multiplicative calculus in biomedical image analysis, J. Math. Imaging Vision, 42 (2012), 64–75.
[7] W. A. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim., 24 (2003), 851–862.
[8] Y. Su, J.-C. Yao, Further generalized contraction mapping principle and best proximity theorem in metric spaces, Fixed Point Theory Appl., 2015 (2015), 13 pages.
[9] J. Zhang, Y. Su, Q. Cheng, A note on ‘A best proximity point theorem for Geraghty-contractions’, Fixed Point Theory Appl., 2013 (2013), 4 pages.
[10] J. Zhang, Y. Su, Q. Cheng, Best proximity point theorems for generalized contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), 7 pages.