A coincidence-point problem of Perov type on rectangular cone metric spaces

Volume 10, Issue 8, pp 4307--4317 http://dx.doi.org/10.22436/jnsa.010.08.25

Publication Date: August 22, 2017 Submission Date: March 11, 2017

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)

• 2110 Downloads
• 2911 Views

Authors

Fairouz Tchier - Mathematics Department College of Science (Malaz), King Saud University, P. O. Box 22452, Riyadh, King Saudi Arabia. Calogero Vetro - Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy. Francesca Vetro - Department of Energy, Information Engineering and Mathematical Models (DEIM), University of Palermo, Viale delle Scienze, 90128 Palermo, Italy.

Abstract

We consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using \(\alpha\)-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.

Share and Cite

Keywords

• Rectangular cone metric space
• spectral radius
• solid cone
• \(g-\)contraction of Perov type
• \(\alpha\)-admissible mapping
• \(\alpha-g-\)contraction of Perov type.

MSC

•  47H10
•  54H25

References

• [1] M. Abbas, V. Rakočević, A. Iqbal , Coincidence and common fixed points of Perov type generalized Ćirić-contraction mappings, Mediterr. J. Math., 13 (2016), 3537–3555.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] M. Abbas, V. Rakočević, A. Iqbal , Fixed points of Perov type contractive mappings on the set endowed with a graphic structure, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM, (2017), 1–20.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] J. Ahmad, M. Arshad, C. Vetro, On a theorem of Khan in a generalized metric space, Int. J. Anal., 2013 (2013), 6 pages.
  • MathSciNet


• [4] C. D. Aliprantis, R. Tourky , Cones and duality, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (2007)
  • Google Scholar


• [5] A. Azam, M. Arshad, I. Beg, Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math., 3 (2009), 236–241.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181.
  • Google Scholar


• [7] A. Branciari , A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31–37.
  • MathSciNet
  • Google Scholar
  • MATH


• [8] M. Cvetković, V. Rakočević, Common fixed point results for mappings of Perov type, Math. Nachr., 288 (2015), 1873– 1890.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin (1985)


• [10] C. Di Bari, P. Vetro , Common fixed points in generalized metric spaces, Appl. Math. Comput., 218 (2012), 7322–7325.
  • View Article
  • Google Scholar


• [11] L.-G. Huang, X. Zhang , Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468–1476.
  • View Article
  • Google Scholar


• [12] Z. Kadelburg, S. Radenović, Fixed point results in generalized metric spaces without Hausdorff property, Math. Sci. (Springer), 8 (2014), 8 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] Z. Kadelburg, S. Radenović, On generalized metric spaces: a survey , TWMS J. Pure Appl. Math., 5 (2014), 3–13.
  • MathSciNet
  • Google Scholar
  • MATH


• [14] P. Kumam, C. Vetro, F. Vetro, Fixed points for weak \(\alpha-\psi\)-contractions in partial metric spaces, Abstr. Appl. Anal., 2013 (2013), 9 pages.
  • View Article
  • Google Scholar


• [15] V. La Rosa, P. Vetro, Common fixed points for \(\alpha-\psi-\phi\)-contractions in generalized metric spaces, Nonlinear Anal. Model. Control, 19 (2014), 43–54.
  • Google Scholar


• [16] S. K. Malhotra, S. Shukla, R. Sen, Some fixed point theorems for ordered Reich type contractions in cone rectangular metric spaces,, Acta Math. Univ. Comenian. (N.S.), 82 (2013), 165–175.
  • MathSciNet
  • Google Scholar
  • MATH


• [17] A. I. Perov, On the Cauchy problem for a system of ordinary differential equations, (Russian) Približ. Metod. Rešen. Differencial’. Uravnen. Vyp., 2 (1964), 115–134.


• [18] A. I. Perov, A. V. Kibenko, On a certain general method for investigation of boundary value problems, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 30 (1966), 249–264.
  • MathSciNet
  • Google Scholar


• [19] B. Samet , Discussion on ”A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces” by A. Branciari [ MR1771669], Publ. Math. Debrecen, 76 (2010), 493–494.
  • MathSciNet
  • Google Scholar
  • MATH


• [20] B. Samet, C. Vetro, P. Vetro , Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154–2165.
  • View Article
  • Google Scholar


• [21] S. Shukla, Reich type contractions on cone rectangular metric spaces endowed with a graph, Theory Appl. Math. Comput. Sci., 4 (2014), 14–25.
  • Google Scholar
  • MATH


• [22] S. Shukla, S. Balasubramanian, M. Pavlović , A generalized Banach fixed point theorem, Bull. Malays. Math. Sci. Soc., 39 (2016), 1529–1539.
  • View Article
  • MathSciNet
  • Google Scholar


• [23] P. Vetro , Common fixed points in cone metric spaces , Rend. Circ. Mat. Palermo, 56 (2007), 464–468.
  • View Article
  • Google Scholar


• [24] C. Vetro, On Branciari’s theorem for weakly compatible mappings, Appl. Math. Lett., 23 (2010), 700–705.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] Y. C.Wong, K. F. Ng, Partially ordered topological vector spaces, Oxford Mathematical Monographs, Clarendon Press, Oxford (1973)
  • Google Scholar


• [26] S.-Y. Xu, Ć . Dolićanin, S. Radenović, Some remarks on results of Perov type, J. Adv. Math. Stud., 9 (2016), 361–369.
  • MathSciNet
  • Google Scholar
  • MATH


• [27] P. P. Zabrejko, K-metric and K-normed linear spaces: survey, Fourth International Conference on Function Spaces, Zielona Góra, (1995), Collect. Math., 48 (1997), 825–859.
  • MathSciNet
  • Google Scholar
  • MATH