Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171203Contractive gauge functions in strongly orthogonal metric spaces232845210.22075/ijnaa.2016.452ENMaryam RamezaniDepartment of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, IranHamid BaghaniDepartment of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, IranJournal Article20151107Existence 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.http://ijnaa.semnan.ac.ir/article_452_2a1a25491ed3b19576dc43dcff80d39b.pdf