University of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Fixed Point Theory in $\varepsilon$-connected Orthogonal Metric Space35463636610.22130/scma.2018.72368.289ENMadjidEshaghi GordjiDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran.HastiHabibiDepartment of Mathematics, Semnan University, Semnan, Iran.Journal Article20170923The 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.https://scma.maragheh.ac.ir/article_36366_988f1f54affa1680ce562c8d50a002e5.pdf