Fixed Point Results for Generalized Contraction Mappings and Cyclical Mappings in b-Metric Spaces Endowed with a Digraph

Sushanta Kumar Mohanta; Deep Biswas

doi:10.2478/awutm-2019-0017

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Fixed Point Results for Generalized Contraction Mappings and Cyclical Mappings in b-Metric Spaces Endowed with a Digraph

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 57 (2019): Issue 2 (December 2019)

By: Sushanta Kumar Mohanta and Deep Biswas

Open Access

|Dec 2020

Abstract

In this paper, we establish a fixed point theorem for generalized contraction mappings in b-metric spaces endowed with a digraph. As an application of this result, we obtain fixed points of cyclical mappings in the setting of b-metric spaces. Our results extend and generalize several existing results in the literature.

References

[1] S. Aleomraninejad, S. Rezapour, and N. Shahzad, Fixed point results on subgraphs of directed graphs, Mathematical Sciences, 2013, (2013), 7:4110.1186/2251-7456-7-41
Search in Google Scholar Back to article
[2] M. R. Alfuraidan and M. A. Khamsi, Caristi fixed point theorem in metric spaces with a graph, Abstract and Applied Analysis, 2014, (2014), Article ID 30348410.1186/1687-1812-2014-240
Search in Google Scholar Back to article
[3] I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., Gos. Ped. Inst. Unianowsk, 30, (1989), 26-37
Search in Google Scholar Back to article
[4] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3, (1922), 133-18110.4064/fm-3-1-133-181
Search in Google Scholar Back to article
[5] J. A. Bondy and U. S. R. Murty, Graph theory with applications,American Elsevier Publishing Co., Inc., New York, 197610.1007/978-1-349-03521-2
Search in Google Scholar Back to article
[6] I. Beg,A.R.Butt, andS.Radojevic, The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl., 60, (2010), 1214-121910.1016/j.camwa.2010.06.003
Search in Google Scholar Back to article
[7] F. Bojor, Fixed point of φ-contraction in metric spaces endowed with a graph, Annals of the University of Craiova, Mathematics and Computer Science Series, 37, (2010), 85-92
Search in Google Scholar Back to article
[8] F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. St. Univ. Ovidius Constanta, 20, (2012), 31-4010.2478/v10309-012-0003-x
Search in Google Scholar Back to article
[9] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4, (2009), 285-301
Search in Google Scholar Back to article
[10] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav, 1, (1993), 5-11
Search in Google Scholar Back to article
[11] G. Chartrand, L. Lesniak, and P. Zhang, Graph and digraph, CRC Press, New York, NY, USA, 2011
Search in Google Scholar Back to article
[12] F. Echenique, A short and constructive proof of Tarski’s fixed point theorem, Internat. J. Game Theory, 33, (2005), 215-21810.1007/s001820400192
Search in Google Scholar Back to article
[13] R. Espinola and W. A. Kirk, Fixed point theorems in R-trees with applications to graph theory, Topology Appl., 153, (2006), 1046-105510.1016/j.topol.2005.03.001
Search in Google Scholar Back to article
[14] J. I. Gross and J. Yellen, Graph theory and its applications, CRC Press, New York, NY, USA, 1999
Search in Google Scholar Back to article
[15] N. Hussain, R. Saadati, and R. P. Agrawal, On the topology and wt-distance on metric type spaces, Fixed Point Theory and Applications, 2014, (2014), 8810.1186/1687-1812-2014-88
Search in Google Scholar Back to article
[16] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136, (2008), 1359-137310.1090/S0002-9939-07-09110-1
Search in Google Scholar Back to article
[17] M. A. Khamsi and N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73, (2010), 3123-312910.1016/j.na.2010.06.084
Search in Google Scholar Back to article
[18] W. A. Kirk, P. S. Srinivasan, and P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4, (2003), 79-89
Search in Google Scholar Back to article
[19] P. Kaushik and S. Kumar, Fixed point results for (α, ψ, ξ)-contractive compatible multi-valued mappings, Journal of Nonlinear Analysis and Applications, 2016, (2016), doi:10.5899/2016/jnaa-0030510.5899/2016/jnaa-00305
Search in Google Scholar Back to article
[20] S. K. Mohanta,Commonfixedpointsin b-metric spaces endowed with a graph, Math. Vesnik, 68, (2016), 140-154
Search in Google Scholar Back to article
[21] J. J. Nieto and R. R. López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin.(Engl. Ser.), 23, (2007), 2205-221210.1007/s10114-005-0769-0
Search in Google Scholar Back to article
[22] M. Păcurar and I. A. Rus, Fixed point theory for cyclic φ-contractions, Nonlinear Anal., 72, (2010), 1181-118710.1016/j.na.2009.08.002
Search in Google Scholar Back to article
[23] M. A. Petric, Some results concerning cyclical contractive mappings, General Mathematics, 18, (2010), 213-226
Search in Google Scholar Back to article
[24] I. A. Rus, Cyclic representations and fixed points, Ann. T. Popoviciu Seminar Funct. Eq. Approx. Convexity, 3, (2005), 171-178
Search in Google Scholar Back to article
[25] J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, and W. Shatanawi, Common fixed points of almost generalized (ψ, φ)_s-contractive mappings in ordered b-metric spaces, Fixed Point Theory and Applications, 2013, (2013), 15910.1186/1687-1812-2013-130
Search in Google Scholar Back to article
[26] B. Samet and M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Communications in Mathematical Analysis, 13, (2012), 82-97
Search in Google Scholar Back to article
[27] J. Tiammee and S. Suantal, Coincidence point theorems for graph-preserving multi-valued mappings, Fixed Point Theory and Applications, 2014, (2014), 2014:7010.1186/1687-1812-2014-70
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/awutm-2019-0017 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

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Language: English

Page range: 86 - 102

Published on: Dec 21, 2020

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

digraph,

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© 2020 Sushanta Kumar Mohanta, Deep Biswas, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 57 (2019): Issue 2 (December 2019)