Fixed point belonging to the zero-set of a given function

Volume 11, Issue 3, pp 417--424 http://dx.doi.org/10.22436/jnsa.011.03.09

Publication Date: February 22, 2018 Submission Date: October 30, 2017 Revision Date: December 28, 2017 Accteptance Date: December 31, 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)

• 2197 Downloads
• 3769 Views

Authors

Francesca Vetro - Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam. - Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.

Abstract

We prove the existence and uniqueness of fixed point belonging to the zero-set of a given function. The results are established in the setting of metric spaces and partial metric spaces. Our approach combines the recent notions of \((F,\varphi)\)-contraction and \(\mathcal{Z}\)-contraction. The main result allows to deduce, as a particular case, some of the most known results in the literature. An example supports the theory.

Share and Cite

Keywords

• Fixed point
• metric space
• partial metric space
• nonlinear contraction
• simulation function

MSC

•  47H10
•  54H25

References

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


• [2] D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458–464
  • Google Scholar


• [3] M. Jleli, B. Samet, C. Vetro, Fixed point theory in partial metric spaces via \(\varphi\)-fixed point’s concept in metric spaces, J. Inequal. Appl., 2014 (2014), 9 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (2015), 1189–1194


• [5] S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728 (1994), 183–197
  • View Article
  • MathSciNet
  • Google Scholar


• [6] S. J. O’Neill, Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. , 806 (1996), 304–315
  • View Article
  • MathSciNet
  • Google Scholar


• [7] D. Paesano, P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911–920
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] S. Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital., 5 (1972), 26–42
  • Google Scholar


• [9] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683–2693
  • View Article
  • MathSciNet
  • Google Scholar


• [10] B. Samet, C. Vetro, F. Vetro, From metric spaces to partial metric spaces, Fixed Point Theory Appl., 2013 (2013 ), 11 pages
  • View Article
  • MathSciNet


• [11] 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