Coupled fixed point results for (\(\varphi,G\))-contractions of type (b) in b-metric spaces endowed with a graph

Volume 10, Issue 2, pp 671--683 http://dx.doi.org/10.22436/jnsa.010.02.29

Publication Date: February 20, 2017 Submission Date: June 06, 2016

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2076 Downloads
• 3441 Views

Authors

Cristian Chifu - Faculty of Business, Babeş-Bolyai University Cluj-Napoca, Cluj-Napoca, Romania. Gabriela Petrusel - Faculty of Business, Babeş-Bolyai University Cluj-Napoca, Cluj-Napoca, Romania.

Abstract

The purpose of this paper is to present some existence results for coupled fixed points of generalized contraction type operators in b-metric spaces endowed with a directed graph. Our results generalize the results obtained by Gnana Bhaskar and Lakshmikantham in [T. Gnana Bhaskar, V. Lakshmikantham, Nonlinear Anal., 65 (2006), 1379–1393]. Data dependence, well-posednes and Ulam-Hyres stability of the fixed point problem are also studied.

Share and Cite

Keywords

• Fixed point
• coupled fixed point
• b-metric space
• connected graph.

MSC

•  47H10
•  54H25

References

• [1] I. Beg, A. R. Butt, S. Radojević, The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl., 60 (2010), 1214–1219.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, ”Babe-Bolyai” Univ., Cluj-Napoca, (1993), 3–9.
  • MathSciNet
  • Google Scholar


• [3] V. Berinde, Sequences of operators and fixed points in quasimetric spaces, Studia Univ. Babeş-Bolyai Math., 41 (1996), 23–27.
  • MathSciNet
  • MATH


• [4] V. Berinde, Contracţii generalizate şi aplicaţii, (Romanian) [[Generalized contractions and applications]] Colecia Universitaria (Baia Mare) [University Collection], Editura Cub Press 22, Baia Mare (1997)
  • MathSciNet
  • MATH


• [5] I. C. Chifu, G. Petruşel, Generalized contractions in metric spaces endowed with a graph, Fixed Point Theory Appl., 2012 (2012 ), 9 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] I. C. Chifu, G. Petruşel, New results on coupled fixed point theory in metric spaces endowed with a directed graph, Fixed Point Theory Appl., 2014 (2014 ), 13 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263–276.
  • MathSciNet
  • Google Scholar


• [8] T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379–1393.
  • View Article
  • Google Scholar


• [9] G. Gwóźdź-Łukawska, J. Jachymski, IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem, J. Math. Anal. Appl., 356 (2009), 453–463.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. , 71 (2009), 3403–3410.
  • View Article
  • MathSciNet
  • Google Scholar


• [11] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359–1373.
  • View Article
  • MathSciNet
  • Google Scholar


• [12] J. Jachymski, J. Klima, Around Perov’s fixed point theorem for mappings on generalized metric spaces, Fixed Point Theory, 17 (2016), 367–380.
  • MathSciNet
  • Google Scholar
  • MATH


• [13] M. Jleli, B. Samet, C. Vetro, F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstr. Appl. Anal., 2015 (2015 ), 7 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223–239.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] J. J. Nieto, R. L. Pouso, R. Rodríguez-López, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc., 135 (2007), 2505–2517.
  • View Article
  • MathSciNet


• [16] J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205–2212.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] D. O’Regan, A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241–1252.
  • View Article
  • Google Scholar


• [18] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435–1443.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] C. Vetro, F. Vetro, Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results, Topology Appl., 164 (2014), 125–137.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH