Discussion on ordered fixed point results and related applications

Document Type : Review articles


1 Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

2 Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran

3 Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran


The aim of this manuscript is to introduce the notion of ℜ-extended b-metric spaces and prove some fixed point results in this space.  An extensive set of nontrivial examples is given to justify the claims.


[1] M. U. Ali, Y. Guo, F. Uddin, H. Aydi, K. Javed and Z. Ma, On partial metric spaces and related fixed point
results with applications, J. Funct. Spaces 2020 (2020), Article ID 6671828[2] H. Baghani and M. Ramezani, A fixed point theorem for a new class of set valued mappings in ℜ-complete (not
necessarily complete) metric spaces, Filomat 31 (2017), 3875–3884.
[3] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. 30 (1989), 26–37.
[4] M. Boriceanu, M. Bota and A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math. 8 (2010),
no. 2, 367–377.
[5] N. Bourbaki, Topologie generale, Herman, Paris, France, 1974.
[6] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostra. 1 (1993), 5–11.
[7] K. Javed, F. Uddin, H. Aydi, A. Mukheimer and M. Arshad, Ordered-theoretic fixed point results in fuzzy b-metric
spaces with an application, J. Math 2021 (2021), Article ID 6663707.
[8] T. Kamran, M. Samreen and Q.U. Ain, A generalization of b-metric space and some fixed point theorems, Math.
5 (2017), no. 2, 19.
[9] S. Khalehoghli, H. Rahimi and M. Eshagahi Gordji, Fixed point theorem in ℜ-metric spaces with applications,
AIMS Math. 5 (2020), no. 4, 3125–3137.
[10] R.D. Maddux, Topics in relation algebras, University of California, Berkeley, 1978.
[11] V. Parvaneh and Z. Kadelburg, Fixed points of JSHR-contractive type mappings in extended b-metric-like spaces,
Viet. J. Math. 47 (2019), no. 2, 387–401.
[12] V. Parvaneh and Z. Kadelburg, Extended partial b-metric spaces and some fixed point results, Filomat 32 (2018),
no. 8, 2837–2850.
[13] V. Parvaneh, N. Hussain, and Z. Kadelburg, Generalized Wardowski type fixed point theorems via α-admissible
F G-contractions in b-metric spaces, Acta Math. Sci. 36 (2016), no. 5, 1445–1456.
[14] S.S. Razavi and H.P. Masiha, Some fixed point results on new Generalization of Metric Spaces by Orthogonal
properties with Application for some Ordinary Differential Equation, J. Math. Anal. 9 (2018), no. 1, 29–37.
[15] J.R. Roshan, N. Shobkolaei, S. Sedghi, V. Parvaneh and S. Radenovi´c, Common fixed point theorems for three
maps in discontinuous Gb metric spaces, Acta Math. Sci. 34 (2019), no. 5, 1643–1654.
[16] B. Samet and M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relations
and applications, Common. Math. Anal. 13 (2012), 82–97.
Volume 13, Issue 2
July 2022
Pages 999-1008
  • Receive Date: 12 August 2021
  • Revise Date: 02 September 2021
  • Accept Date: 04 September 2021