Abstract—In this paper, we introduce the notion of orthogonal Z-contraction mappings and prove fixed point theorems for such contraction mappings in orthogonally metric spaces, which are generalizations of fixed point results for Z-contraction mappings in metric spaces. As an application, we apply our main results to show the existence of a unique positive definite solution of a nonlinear matrix equation.

Index Terms—Fixed point, orthogonally metric spaces, Z-contraction mappings.

The authors are with Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12120, Thailand (email: juneks.ks@gmail.com).

Cite: Kanokwan Sawangsup, Wutiphol Sintunavarat, "Fixed Point Results for Orthogonal Z-Contraction Mappings in O-Complete Metric Spaces," International Journal of Applied Physics and Mathematics vol. 10, no. 1, pp. 33-40, 2020.

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