On some recent fixed point results for (\(\psi,\varphi\))-contractive mappings in ordered partial b-metric spaces

Volume 9, Issue 7, pp 4990--4999 http://dx.doi.org/10.22436/jnsa.009.07.03

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)

• 2099 Downloads
• 4212 Views

Authors

Huaping Huang - School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China. Diana Dolićanin-Đekić - Faculty of Technical Sciences, University of Prištna-Kosovska Mitrovica, Serbia. Guantie Deng - School of Mathematical Sciences, Beijing Normal University, Beijing, Beijing, 100875, China.

Abstract

In this paper we unite, complement, improve, and generalize the recent fixed point results in ordered partial b-metric spaces, established by Mustafa et al. [Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, J. Inequal. Appl., 2013 (2013), 26 pages], with much shorter proofs. An example is given to show the superiority of the results obtained.

Share and Cite

Keywords

• Fixed point
• b-metric space
• partial metric space
• ordered partial b-metric space
• partially ordered set.

MSC

•  47H10
•  54H25

References

• [1] M. Abbas, V. Parvaneh, A. Razani, Periodic points of T-Ciric generalized contraction mappings in ordered metric spaces, Georgian Math. J., 19 (2012), 597--610


• [2] A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941--960


• [3] J. Ahmad, A. Azam, M. Arshad, Fixed points of multivalued mappings in partial metric spaces, Fixed Point Theory and Appl., 2013 (2013), 9 pages


• [4] A. Azam, N. Mehmood, J. Ahmad, S. Radenovic, Multivalued fixed point theorems in cone b-metric spaces, J. Inequal. Appl., 2013 (2013), 9 pages


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


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


• [7] D. Đorić, Common fixed point for generalized (\(\psi,\phi\))-weak contractions, Appl. Math. Lett., 22 (2009), 1896--1900


• [8] X. Ge, S. Lin, A note on partial b-metric spaces, Mediterr. J. Math., 13 (2016), 1273--1276


• [9] R. H. Haghi, Sh. Rezapour, N. Shahzad, Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450--454


• [10] H. Huang, J. Vujaković, S. Radenović, A note on common fixed point theorems for isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 808--815


• [11] N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic weakly ( \(\psi,\varphi,L, A,B\))-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory and Appl., 2013 (2013), 18 pages


• [12] N. Hussain, J. R. Roshan, V. Parvaneh, A. Latif, A unification of G-metric, partial metric, and b-metric spaces, Abstr. Appl. Anal., 2014 (2014), 14 pages


• [13] N. Hussain, R. Saadati, R. P. Agarwal, On the topology and wt-distance on metric type spaces, Fixed Point Theory and Appl., 2014 (2014), 14 pages


• [14] M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1--9


• [15] M. A. Kutbi, J. Ahmad, N. Hussain, M. Arshad, Common fixed point results for mappings with rational expressions, , 2013 (2013), 11 pages


• [16] S. G. Matthews, Partial metric topology, Papers on general topology and applications, Ann. New York Acad. Sci., 728 (1994), 183--197


• [17] A. Mukheimer, \(\alpha-\psi-\phi\)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 168--179


• [18] Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl., 2013 (2013), 26 pages


• [19] H. K. Nashine, Z. Kadelburg, S. Radenović, Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces, Math. Comput. Modelling, 57 (2013), 2355--2365


• [20] J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223--239


• [21] 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


• [22] V. Parvaneh, J. R. Roshan, S. Radenović, Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations, Fixed Point Theory and Appl., 2013 (2013), 19 pages


• [23] O. Popescu, Fixed points for (\(\psi,\phi\))-weak contractions, Appl. Math. Lett., 24 (2011), 1--4


• [24] S. Radenović, Coincidence point results for nonlinear contraction in ordered partial metric spaces, J. Indian Math. Soc. (N.S.), 81 (2014), 319--333


• [25] 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


• [26] J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi)_s\)-contractive mappings in ordered b-metric spaces, Fixed Point Theory and Appl., 2013 (2013), 123 pages


• [27] P. Salimi, N. Hussain, S. Shukla, Sh. Fathollahi, S. Radenović, Fixed point results for cyclic \(\alpha-\psi\varphi\)-contractions with application to integral equations, J. Comput. Appl. Math., 290 (2015), 445--458


• [28] S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math., 11 (2014), 703--711