# Fixed point theorems for $(\alpha,\beta)-(\psi,\varphi)$-contractive mapping in b--metric spaces with some numerical results and applications

Volume 9, Issue 1, pp 22--33
• 1444 Views

### Authors

Oratai Yamaod - Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand. Wutiphol Sintunavarat - Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand.

### Abstract

In this paper, we introduce the concept of $(\alpha,\beta)-(\psi,\varphi)$-contractive mapping in b-metric spaces. We establish some fixed point theorems for such mappings and also give an example supporting our results. Finally, we apply our main results to prove a fixed point theorem involving a cyclic mapping.

### Share and Cite

##### ISRP Style

Oratai Yamaod, Wutiphol Sintunavarat, Fixed point theorems for $(\alpha,\beta)-(\psi,\varphi)$-contractive mapping in b--metric spaces with some numerical results and applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 1, 22--33

##### AMA Style

Yamaod Oratai, Sintunavarat Wutiphol, Fixed point theorems for $(\alpha,\beta)-(\psi,\varphi)$-contractive mapping in b--metric spaces with some numerical results and applications. J. Nonlinear Sci. Appl. (2016); 9(1):22--33

##### Chicago/Turabian Style

Yamaod, Oratai, Sintunavarat, Wutiphol. "Fixed point theorems for $(\alpha,\beta)-(\psi,\varphi)$-contractive mapping in b--metric spaces with some numerical results and applications." Journal of Nonlinear Sciences and Applications, 9, no. 1 (2016): 22--33

### Keywords

• $b$-metric space
• cyclic $(\alpha،\beta)$-admissible mapping
• $(\alpha،\beta)-(\psi،\varphi)$-contractive mapping.

•  47H09
•  47H10

### References

• [1] A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941-960.

• [2] S. Alizadeh, F. Moradlou, P. Salimi, Some fixed point results for $(\alpha,\beta)-(\psi,\phi)$-contractive mappings, Filomat, 28 (2014), 635-647.

• [3] M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math, 8 (2010), 367-377.

• [4] M. Bota, A. Molnar, V. Csaba, On Ekeland's variational principle in b-metric spaces, Fixed Point Theory, 12 (2011), 21-28.

• [5] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.

• [6] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263-276.

• [7] M. S. Khan, M. Swaleh, S. Sessa , Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9.

• [8] W. A. Kirk, P. S. Srinivasan, P. Veeramani , Fixed points for mappings satisfying cyclical contractive conditions , Fixed Point Theory, 4 (2003), 79-89.