Document Type : Research Paper

Authors

• Maryam Ramezani ¹
• Hamid Baghani ²

¹ Department of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, Iran

² Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran

Abstract

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.

Keywords

• strongly orthogonal set
• Fixed point
• gauge function