International Journal of Nonlinear Analysis and Applications

Banach fixed point theorem on incomplete orthogonal S-metric spaces

Document Type : Research Paper

Authors

1 Departmen of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Semnan University, Semnan, Iran

3 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

In this paper, we are interested in obtaining fixed point theorem for mappings in S-metric space by wearing the completeness of S-metric space using relations. As consequences, an application to existence and uniqueness of solution of integral equation is given.

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), no. 3, 465–477.

[2] 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), no. 2, 569–578.

[3] M. Eshaghi and H. Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Topol. Algebr. 6 (2017), no. 3, 251–260.

[4] M. Eshaghi, H. Habibi and M. B. Sahabi, Orthogonal sets; orthogonal contractions, Asian-European J. Math. 12 (2019), no. 3, 1950034.

[5] M. Eshaghi and H. Habibi, Existence and uniqueness of solutions to a first-order differential equation via fixed point theorem in orthogonal metric space,Facta Univ. Ser. Math. Inf. 34 (2019), 123–135.

[6] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), 289–297.

[7] Z. Mustafa, H. Obiedat and F. Awawdeh, Some common fixed point theorems for mapping on complete G-metric spaces, Fixed Point Theory Appl. 2008 (2008), Article ID 189870.
[8] Z. Mustafa and B. Sims, Some results concerning D-metric spaces, Proc. Int. Conf. Fixed Point Theory Appl. Valencia, Spain, 2003, pp. 189–198.

[9] N.Y. Ozgur and N.Tas, Some fixed theorems on s-metric spaces, Mat. Vesnik. 69 (2017), no. 1, 39–52.

[10] S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorems in s-metric spaces, Mat. Vesnik. 64 (2012), no. 3, 258–266.

[11] S. Sedghi, N. Shobe and H. Zhou, A common fixed point theorem in D∗ -metric spaces, Fixed Point Theory Appl.
2007 (2007), Article ID 27906, 13 pages.

[12] M. Ramezani and H. Baghani, The Meir–Keeler fixed point theorem in incomplete modular spaces with application, J. Fixed Point Theory Appl. 19 (2017), no. 4, 2369–2382.

[13] A. Bahraini, G. Askari, M. Eshaghi Gordji and R. Gholami, Stability and hyperstability of orthogonally ∗ mhomomorphisms in orthogonally Lie C∗-algebras: a fixed point approach, J. Fixed Point Theory Appl. 20 (2018), no. 2, 1- 12.

[14] M. Ramezani and H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl. 8 (2017), no. 2, 23–28.

[15] M. Ramezani, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl. 6 (2015), no. 2, 127–132.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 2
February 2023
Pages 151-157
  • Receive Date: 09 December 2020
  • Revise Date: 30 December 2020
  • Accept Date: 12 November 2021