Coincidence point theorems in quasi-ordered $\mathcal{F}$-metric spaces and its application

Subject Areas : Operator theory

H. Majani ^{1 *}

1 - Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Received: 2024-12-12 Accepted : 2025-03-15 Published : 2025-03-17

Keywords: quasi-ordered F-metric spaces, coincidence point, coupled coincidence point, mixed g-monotone property, integral equation,

Abstract :

The main goal of this article is to demonstrate the existence of a (couple) coincidence point for an infinite family of mappings in quasi-ordered $\mathcal{F}$-metric spaces. Some consequences are also added, along with an example and an application, to show the efficiency of the obtained results.

References:

[1] M. Abbas, M. Ali Khan, S. Radenovi´ c, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput. 217 (1) (2010), 195-202.

[2] O. Alqahtani, E. Karapınar, P. Shahi, Common fixed point results in function weighted metric spaces, J. Inequal. Appl. (2019), 2019:164.

[3] H. Aydi, E. Karapınar, Z. D. Mitrovi´ c, T. Rashid, A remark on “Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results F-metric spaces”, RACSAM. 113 (4) (2019), 3197-3206.

[4] A. Bera, H. Garai, B. Damjanovi´ c, A. Chanda, Some interesting results on F-metric spaces, Filomat. 33 (10) (2019), 3257-3268.

[5] T. G. Bhaskar, V. Lakshmikantham, Fixed point theory in partially ordered metric spaces and applications. Nonlinear Anal. 65 (2006), 1379-1393.

[6] E. L. Ghasab, H. Majani, E. Karapınar, G. Soleimani Rad, New fixed point results in F-quasi-metric spaces and an application, Adv. Math. Phys. (2020), 2020:9452350.

[7] E. L. Ghasab, H. Majani, G. Soleimani Rad, Fixed points of set-valued F-contraction operators in quasi-ordered metric spaces with an application to integral equations, J. Sib. Fed. Univ. Math. Phys. 14 (2) (2021), 150-158.

[8] E. Lotfali Ghasab, H. Majani, G. Soleimani Rad, Integral type contraction and coupled fixed point theorems in ordered G-metric spaces, J. Linear. Topological. Algebra. 9 (2) (2020), 113-120.

[9] B. Hazarika, R. Arab, P. Kumam, Coupled fixed point theorems in partially ordered metric spaces via mixed g-monotone property, J. Fixed Point Theory Appl. (2019), 21:1.

[10] M. Jleli, B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory and Appl. (2018), 20:128.

[11] V. Lakshmikantham, L.´Ciri´ c, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (12) (2009), 4341-4349.

[12] H. Rahimi, P. Vetro, G. S. Rad, Coupled fixed-point results for T-contractions on cone metric spaces with applications, Math. Notes. 98 (2015), 158-167.

[13] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443.

[14] W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Model. 55 (34) (2012), 680-687.

[15] G. Soleimani Rad, S. Shukla, H. Rahimi, Some relations between n-tuple fixed point and fixed point results, RACSAM. 109 (2) (2015), 471-481.