1. bookVolume 57 (2019): Issue 2 (December 2019)
Journal Details
License
Format
Journal
eISSN
1841-3307
First Published
22 Nov 2012
Publication timeframe
2 times per year
Languages
English
Open Access

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

Published Online: 21 Dec 2020
Volume & Issue: Volume 57 (2019) - Issue 2 (December 2019)
Page range: 86 - 102
Journal Details
License
Format
Journal
eISSN
1841-3307
First Published
22 Nov 2012
Publication timeframe
2 times per year
Languages
English

[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

[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

[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

[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

[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

[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

[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

[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

[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

[10] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav, 1, (1993), 5-11 Search in Google Scholar

[11] G. Chartrand, L. Lesniak, and P. Zhang, Graph and digraph, CRC Press, New York, NY, USA, 2011 Search in Google Scholar

[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

[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

[14] J. I. Gross and J. Yellen, Graph theory and its applications, CRC Press, New York, NY, USA, 1999 Search in Google Scholar

[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

[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

[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

[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

[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

[20] S. K. Mohanta,Commonfixedpointsin b-metric spaces endowed with a graph, Math. Vesnik, 68, (2016), 140-154 Search in Google Scholar

[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

[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

[23] M. A. Petric, Some results concerning cyclical contractive mappings, General Mathematics, 18, (2010), 213-226 Search in Google Scholar

[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

[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

[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

[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

Recommended articles from Trend MD

Plan your remote conference with Sciendo