Rectangular b-metric space and contraction principles

Volume 8, Issue 6, pp 1005--1013 http://dx.doi.org/10.22436/jnsa.008.06.11

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)

• 6507 Downloads
• 7645 Views

Authors

R. George - Department of Mathematics and Computer Science, St. Thomas College, Bhilai, Chhattisgarh, India. S. Radenović - Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia. K. P. Reshma - Department of Mathematics, Government VYT PG Autonomous College, Durg, Chhattisgarh, India. S. Shukla - Department of Applied Mathematics, S.V.I.T.S. Indore (M.P.), India.

Abstract

The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.

Share and Cite

Keywords

• Fixed points
• b-metric space
• rectangular metric space
• rectangular b-metric space.

MSC

•  47H10

References

• [1] T. Abdeljawad, D. Turkoglu, Locally convex valued rectangular metric spaces and Kannan's fixed point theorem, arXiv, 2011 (2011), 11 pages.


• [2] H. Aydi, M. F. Bota, E. Karapinar, S. Moradi, A common fixed point for weak \(\phi\)-contractions on b-metric spaces, Fixed Point Theory, 13 (2012), 337-346.


• [3] A. Azam, M. Arshad, Kannan Fixed Point Theorems on generalised metric spaces , J. Nonlinear Sci. Appl., 2008 (1), 45-48.


• [4] A. Azam, M. Arshad, I. Beg, Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math., 3 (2009), 236-241.


• [5] I. A. Bakhtin , The contraction mapping principle in quasimetric spaces , Funct. Anal., Unianowsk Gos. Ped. Inst., 30 (1989), 26-37.


• [6] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces , Inter. J. Mod. Math., 4 (2009), 285-301.


• [7] M. Boriceanu, M. Bota, A. Petrusel, Mutivalued fractals in b-metric spaces, Cen. Eur. J. Math., 8 (2010), 367-377.


• [8] M. Bota, A. Molnar, V. Csaba, On Ekeland's variational principle in b-metric spaces, Fixed Point Theory, 12 (2011), 21-28.


• [9] A. Branciari, A fixed point theorem of Banach-Caccippoli type on a class of generalised metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37.


• [10] C. N. Chen, Common fixed point theorem in complete generalized metric spaces, J. Appl. Math., 2012 (2012), 14 pages.


• [11] S. Czerwik , Contraction mappings in b-metric spaces , Acta. Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.


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


• [13] S. Czerwik, K. Dlutek, S. L. Singh , Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci. , 11 (1997), 87-94.


• [14] S. Czerwik, K. Dlutek, S. L. Singh , Round-off stability of iteration procedures for set valued operators in b-metric spaces, J. Natur. Phys. Sci., 15 (2001), 1-8.


• [15] P. Das, A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sci., 9 (2002), 29-33.


• [16] P. Das, A fixed point theorem in generalized metric spaces , Soochow J. Math., 33 (2007), 33-39.


• [17] P. Das, B. K. Lahri , Fixed point of a Ljubomir Ciric's quasi-contraction mapping in a generalized metric space , Publ. Math. Debrecen, 61 (2002), 589-594.


• [18] P. Das, B. K. Lahri , Fixed Point of contractive mappings in generalised metric space, Math. Slovaca, 59 (2009), 499-504.


• [19] I. M. Erhan, E. Karapinar, T. Sekulic, Fixed Points of (psi, phi) contractions on generalised metric spaces, Fixed Point Theory Appl., 2012 (2012), 12 pages.


• [20] R. George, B. Fisher, Some generalised results of fixed points in cone b-metric spaces , Math. Moravic., 17 (2013), 39-50.


• [21] G. S. Jeong, B. E. Rhoades, Maps for which\( F(T) = F(T^n)\), Fixed Point Theory Appl., 6 (2007), 71-105.


• [22] M. Jleli, B. Samet, The Kannan's fixed point theorem in cone rectangular metric space, J. Nonlinear Sci. Appl., 2 (2009), 161-167.


• [23] H. Lakzian, B. Samet, Fixed Points for (\(\psi,\phi\))-weakly contractive mapping in generalised metric spaces, Appl. Math. Lett., 25 (2012), 902-906.


• [24] S. G. Mathews , Partial Metric Topology, Papers on general topology appl., Ann. New York Acad. Sci., 728 (1994), 183-197.


• [25] D. Mihet, On Kannan fixed point result in generalised metric spaces, J. Nonlinear Sci. Appl., 2 (2009), 92-96.


• [26] I. R. Sarma, J. M. Rao, S. S. Rao, Contractions over generalised metric spaces, J. Nonlinear Sci. Appl., 2 (2009), 180-182.