Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theorem is a real generalization of these fixed point theorems.
Ramezani, M. & Baghani, H. (2017). Contractive gauge functions in strongly orthogonal metric spaces. International Journal of Nonlinear Analysis and Applications, 8(2), 23–28. https://doi.org/10.22075/ijnaa.2016.452
MLA
Ramezani, M., & Baghani, H. "Contractive gauge functions in strongly orthogonal metric spaces", International Journal of Nonlinear Analysis and Applications, 8, 2, 2017, 23–28. doi: 10.22075/ijnaa.2016.452
HARVARD
Ramezani, M., & Baghani, H. (2017). 'Contractive gauge functions in strongly orthogonal metric spaces', International Journal of Nonlinear Analysis and Applications, 8(2), pp. 23–28. doi: 10.22075/ijnaa.2016.452
CHICAGO
Ramezani, M. & Baghani, H., "Contractive gauge functions in strongly orthogonal metric spaces." International Journal of Nonlinear Analysis and Applications, 8 2 (2017): 23–28, doi: 10.22075/ijnaa.2016.452
VANCOUVER
Ramezani M., Baghani H. Contractive gauge functions in strongly orthogonal metric spaces. IJNAA. 2017;8(2):23–28. doi: 10.22075/ijnaa.2016.452
International Journal of Nonlinear Analysis and Applications