Fixed point theory in generalized orthogonal metric space

Subject Areas : Fixed point theory

M. Eshaghi Gordji ¹ , H. Habibi ²

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

Received: 2017-08-06 Accepted : 2017-10-02 Published : 2017-09-01

Keywords: fixed point, Generalized metric space, Orthogonal set, Solution, Cauchy problem,

Abstract :

In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.

References:

[1] H. Baghani, M. Ramezani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl, Article in press.

[2] H. Baghani, M. Eshaghi Gordji, M. Ramezani, Orthogonal sets: their relation to the axiom of choice and a generalized fixed point theorem, J. Fixed Point Theory Appl. 18 (3) (2016), 465-477.

[3] S. Czerwik, K. Krol, Fixed point theorems in generalized metric spaces, Asian-European J. Math. 10 (2) (2017), 1750030.

[4] M. Eshaghi Gordji, M. Ramezani, M. De La Sen, Y. J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory. 18 (2) (2017), 569-578.

[5] A. A. Ivanov, Fixed point theory, J. Sov. Math. 12 (1979), 1-64.

[6] E. Karapinar, Discussion on contractions on generalized metric spaces, Abstract. Appl. Anal. (2014), Article ID 962784, 7 pages.

[7] V. La Rosa, P. Vetro, Common fixed points for α-ψ-ϕ-contractions in generalized metric spaces, Nonlinear Anal. Model. Control. 19 (1) (2014), 43-54.

[8] W. A. J. Luxemburg, On the convegence of successive approximations in the theory of ordinary differential equations. III, Nieun. Arc. Wisk. 6 (1958), 93-98.

[9] M. Ramezani, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl. 6 (2) (2015), 127-132.