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Results in Mathematics

, 74:159 | Cite as

Points of Coincidence That are Zeros of a Given Function

  • Francesca VetroEmail author
Article
  • 65 Downloads

Abstract

We establish results of existence and uniqueness of common fixed point and point of coincidence for two self mappings defined both in a metric space and in a partial metric space. Further, we show that such points are zeros of a given function. Finally, we stress that from our main result it is possible to deduce several well-known results in the literature.

Keywords

Point of coincidence metric space partial metric space nonlinear contraction simulation function 

Mathematics Subject Classification

47H10 54H25 

Notes

References

  1. 1.
    Agarwal, P., Jleli, M., Samet, B. (eds.): On fixed points that belong to the zero set of a certain function. In: Fixed Point Theory in Metric Spaces, pp. 101–122. Springer, Singapore (2018)Google Scholar
  2. 2.
    Argoubi, H., Samet, B., Vetro, C.: Nonlinear contractions involving simulation functions in a metric space with a partial order. J. Nonlinear Sci. Appl. 8(6), 1082–1094 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. 3, 133–181 (1922)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Boyd, D.W., Wong, J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–464 (1969)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jleli, M., Samet, B., Vetro, C.: Fixed point theory in partial metric spaces via \(\varphi \)-fixed point’s concept in metric spaces. J. Inequal. Appl. 2014, 426 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Karapınar, E., Samet, B., Shahi, P.: On common fixed points that belong to the zero set of a certain function. J. Nonlinear Sci. Appl. 10(7), 3447–3455 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Khojasteh, F., Shukla, S., Radenović, S.: A new approach to the study of fixed point theorems via simulation functions. Filomat 29(6), 1189–1194 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Matthews, S.G.: Partial metric topology, In: Proceedings of 8th Summer Conference on General Topology and Applications. Ann. N. Y. Acad. Sci. 728, 183–197 (1994)MathSciNetCrossRefGoogle Scholar
  9. 9.
    O’Neill, S.J.: Partial metrics, valuations and domain theory. In: Proceedings of 11th Summer Conference on General Topology and Applications. Ann. N. Y. Acad. Sci. 806, 304–315 (1996)Google Scholar
  10. 10.
    Paesano, D., Vetro, P.: Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. Topol. Appl. 159, 911–920 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Reich, S.: Fixed points of contractive functions. Boll. Un. Mat. Ital. 5, 26–42 (1972)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Reich, S.: Some remarks concerning contraction mappings. Canad. Math. Bull. 14, 121–124 (1971)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Rhoades, B.E.: Some theorems on weakly contractive maps. Nonlinear Anal. 47, 2683–2693 (2001)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Roldán, A., Karapinar, E., Roldán, C., Martínez-Moreno, J.: Coincidence point theorems on metric spaces via simulation functions. J. Comput. Appl. Math. 275, 345–355 (2015)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Samet, B., Vetro, C., Vetro, F.: From metric spaces to partial metric spaces. Fixed Point Theory Appl. 2013, 5 (2013)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Vetro, C., Vetro, F.: Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results. Topol. Appl. 164, 125–137 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Nonlinear Analysis Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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