Madjid Eshaghi Gordji - Department of Mathematics, Semnan University, P.O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.
Hasti Habibi - Department of Mathematics, Semnan University, Semnan, Iran.

The existence of fixed point in orthogonal metric spaces has been initiated by Eshaghi and et. al [7]. In this paper, we prove existence and uniqueness theorem of fixed point for mappings on $varepsilon$-connected orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point for analytic function of one complex variable. The paper concludes with some illustrating examples.

Fixed point, $varepsilon$-connected, Orthogonal set, solution, Metric space, Analytic function