Document Type: Research Paper

Authors

1 Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran.

2 Department of Mathematics, Semnan University, Semnan, Iran.

10.22130/scma.2018.72368.289

Abstract

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.

Keywords

[1] H. Baghani, M. Eshaghi Gordji, and M. Ramezani, Orthogonal sets: their relation to the axiom of choice and a generalized fixed point theorem, J. Fixed Point Theory Appl., 18 (2016), pp. 465-477.
 
[2] I. Beg and A.R. Butt, Fixed point of set-valued graph contractive mappings, J. Inequa. Appl., (2013), 2013:252.

[3] M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc., 12 (1961), pp. 7-10.

[4] M. Eshaghi Gordji, H. Baghani, H. Khodaei, and M. Ramezani, A generalization of Nadler's fixed point theorem, J. Nonlinear Sci. Appl., 3 (2010), pp. 148-151.

[5] M. Eshaghi Gordji, H. Baghani, H. Khodaei, and M. Ramezani, Generalized multi valued contraction mappings, J. Comput. Anal. Appl., 13 (2011), pp. 730-733.

[6] M. Eshaghi Gordji, H. Baghani, H. Khodaei, and M. Ramezani, Geraghty's fixed point theorem for special multi-valued mappings, Thai. J. Math., 10 (2012), pp. 225-231.

[7] M. Eshaghi Gordji, M. Ramezani, M. De La Sen, and Y.J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18 (2017), pp. 569-578.

[8] R. Espinola, E.S. Kim, and W.A. Kirk, Fixed point properties of mappings satisfying local contractive conditions, Nonlinear Anal. Forum, 6 (2001), pp. 103-111.

[9] N. Mehmood, A. Azam, and S. Aleksic, Topological vector-space valued cone Banach spaces, Int. J. Anal. Appl., 6 (2014), pp. 205-219.

[10] M. Ramezani, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl., 6 (2015), pp. 127-132.

[11] M. Ramezani, H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, International Journal of Nonlinear Analysis and Applications, 8(2) (2017) pp. 23-28.

[12] P. Shahi, J. Kaur, and S.S. Bhatia, On fixed points of generalized $alpha$-$phi$ contractive type mappings in partial metric spaces, Int. J. Anal. Appl., 12 (2016), pp. 38-48.