Contractive gauge functions in strongly orthogonal metric spaces

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.