Sahand Communications in Mathematical Analysis

Perturbed Graphical Metric Spaces and Fixed Point Theory

Document Type : Research Paper

Author

Kamal Fallahi

Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran

https://doi.org/10.22130/scma.2025.2057584.2144
Abstract
Taking into account the recent view of fixed point theory as expressed by Jalali and Samet [On Banach's fixed point theorem in perturbed metric spaces, J. Appl. Anal. Comput.  14 (2) (2025), 992--1001], we first introduce a perturbed metric space equipped with a graph and then present new concepts and notions related to this space. Next, we prove some fixed point theorems related to this new space. Several consequences and an example are also presented to demonstrate the effectiveness of the main results. Following the idea of this article, one can continue this new way to obtain fixed points of the mappings that do not satisfy classic contractions in such spaces endowed with a graph or a partial order.

Keywords

Perturbed graphical metric space
Orbitally $\mathcal{H}$-continuous
Perturbed $\mathcal{H}$-quasi-contractions
Fixed point

Subjects

1. R.P. Agarwal, M. Meehan and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, 2009.
2. S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. J., 3 (1922), pp. 133-181.
3. F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. Şt. Univ. Ovidius Constanţa., 20 (1) (2012), pp. 31-40.
4. F. Bojor, Fixed point theorems for Reich type contractions on a metric spaces with a graph, Nonlinear Anal., 75 (2012), pp. 3895-3901.
5. Lj. B. Ćirić, Generalized contractions and fixed-point theorems, Publ. Inst. Math. (Beograd) (N.S.)., 12 (1971), pp. 19-26.
6. K. Fallahi and A. Aghanians, On quasi-contractions in metric spaces with a graph, Hacet. J. Math. Stat., 45 (2016), pp. 1033-1047.
7. K. Fallahi and G. Soleimani Rad, The Banach type contraction for mappings on algebraic cone metric spaces associated with an algebraic distance and endowed with a Graph, IJMSI., 15 (1) (2020), pp. 41-52.
8. K. Fallahi, G. Soleimani Rad and Z. Kadelburg New fixed point results under generalized c-distance in tvs-cone b-metric spaces with an application to systems of Fredholm integral equations, J. Math. Ext., 12 (1) (2018), pp. 1-19,
9. K. Fallahi, D. Savic and G. Soleimani Rad, The Existence Theorem for Contractive Mappings on wt-distance in b-metric Spaces Endowed with a Graph and its Application, Sahand Commun. Math. Anal., 13 (1) (2019), pp. 1-15.
10. J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), pp. 1359-1373.
11. M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 38 (2014), pp. 1-8.
12. M. Jleli and B. Samet, On Banach’s fixed point theorem in perturbed metric spaces, J. Appl. Anal. Comput., 14 (2) (2025), pp. 992-1001.
13. A. Petruşel and I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 134 (2006), pp. 411-418.
14. A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (5) (2004), pp. 1435-1443.
15. I.A. Rus, A Petruşel and G. Petruşel, Fixed Point Theory, Cluj University Press, Romania, 2008.
16. P.P. Zabrejko, K-metric and K-normed linear spaces:survey, Collect. Math., 48 (5-7) (1997), pp. 825-859.
Sahand Communications in Mathematical Analysis
Volume 23, Issue 1
Winter 2026
Pages 109-121

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