Function weighted $\mathcal{G}$-metric spaces and Hausdorff $\Delta$-distances; an application to fixed point theory

Document Type : Research Paper


Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran


In this paper, we introduce a new space which is a generalization of function weighted metric space introduced by Jleli and Samet [On a new generalization of metric spaces, J. Fixed Point Theory Appl. 2018, 20:128] where namely function weighted $\mathcal{G}$-metric space. Also, a Hausdorff $\Delta$-distance is introduced in these spaces. Then several fixed point results for both single-valued and multi-valued mappings in such spaces are proved. We also construct some examples for the validity of the given results and present an application to the existence of a solution of the Volterra-type integral equation.


[1] M. Abbas, M. Ali Khan and S. Radenovi´c, Common coupled fixed point theorems in cone metric spaces for
w-compatible mappings, Appl. Math. Comput. 217 (2010) 195–202.
[2] O. Alqahtani, E. Karapinar and P. Shahi, Common fixed point results in function weighted metric spaces, J.
Inequal. Appl. 2019 2019 164.
[3] H. Aydi, E. Karapinar, Z. D. Mitrovi´c and 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 and A. Chanda, Some interesting results on F-metric spaces, Filomat 33(10)
(2019) 3257—3268.
[5] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications,
Nonlinear Anal. 65 (2006), 1379–1393.
[6] M. Eshaghi Gordji, H. Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Top. Alg. 6(3)
(2017) 251–260.
[7] E. L. Ghasab, H. Majani, E. Karapinar and G. Soleimani Rad, New fixed point results in F-quasi-metric spaces
and an application, Adv. Math. Phys. 2020 (2020) 9452350.
[8] E. L. Ghasab, H. Majani and G. Soleimani Rad, Integral type contraction and coupled fixed point theorems in
ordered G -metric spaces, J. Linear Top. Alg. 9(2) (2020) 113–120.
[9] M. Jleli and B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018) 128.
[10] S. Khalehoglli, H. Rahimi and M. Eshaghi Gordji, Fixed point theorems in R-metric spaces with applicatications,
AIMS Math. 5(4) (2020) 3125–3137.
[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] Z. D. Mitrovi´c, H. Aydi, N. Hussain and A. Mukheimer, Reich, Jungck, and Berinde common fixed point results
on F-metric spaces and an application, Math. 7 (2019) 387.
[13] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006)
[14] G. Soleimani Rad, S. Shukla and H. Rahimi, Some relations between n-tuple fixed point and fixed point results,
RACSAM. 109 (2) (2015) 471–481.
[15] N. Tahat, H. Aydi, E. Karapinar and W. Shatanawi, Common fixed points for single-valued and multi-valued
maps satisfying a generalized contraction in G-metric spaces, J. Fixed Point Theory Appl. 20121 (2012) 48.
Volume 12, Issue 2
November 2021
Pages 1441-1452
  • Receive Date: 03 June 2020
  • Revise Date: 22 September 2020
  • Accept Date: 28 September 2020