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Abstract

In this paper, the notion of limit property (-Tayyab kamran, 2004-) and common limit property (-Yicheng Liu & Jun Wu & Zhixiang Li, 2005-) for singlevalued and multi-valued mappings on metric spaces are generalized to S-metric spaces. This idea is used to make some common fixed point theorems for singlevalued and multi-valued mappings by using a generalization of coincidence point in S-metric spaces. We give an example of an S-metric which is not continuous.

Keywords

Coincidence point Fixed point Hausdorff S-metric Limit property

Article Details

How to Cite
Pourgholam, A., Sabbaghan, M., & Taleghani, F. (2022). Common Fixed Points of Single-Valued and Multi-Valued Mappings in S-Metric Spaces. Journal of the Indonesian Mathematical Society, 28(1), 19–30. https://doi.org/10.22342/jims.28.1.1106.19-30

References

  1. Afshari, H., Jarad, F., and Abdeljawad, T., ”On a new fixed point theorem with on application on a coupled system of fractional di erential equations”, Adv. Differ. Equ.2020, Article No. 461 (2020), 1-13, https://doi.org/10.1186/s13662-020-02926-0.
  2. Bakhtin, I.A., ”The contraction mapping principal in almost metric spaces”, Funct. Anal., 30 (1989), 26-37.
  3. Baleanu, D., Etemad, S., and Rezapour, S., ”On a fractional hybrid multi-term integrodifferential inclusion with four-point sum and integral boundary conditions”, Adv. Differ. Equ. 2020, Article No. 25 (2020), 1-20, https://doi.org/10.1186/s13662-020-02713-x.
  4. Dhage, B.C., ”Generalized metric spaces mappings with fixed point”, Bull. Cal. Math. Soc., 84 (1992), 329-336.
  5. Dung, N.V., and Hieu, S. Radojevic, N.T., ”Fixed point theorems for g-monotone maps on partially ordered S-metric spaces”, Filomat, (2014), 1885-1898.
  6. Etemad, S., Hussain, A., Imran, A., Alzabut, J., Rezapour, S., and George, A., ”On a fractional cantilever beam model in the q-difference inclusion settings via special multi-valued operators”, J Inequal Appl 2021, Article No. 174 (2021), 1-20, https://doi.org/10.1186/s13660-021-02708-6.
  7. S. Etemad, Rezapour, S., and Samei, M.E., ”α−ψ-contractions and solutions of a q-fractional differential inclusion with three-point boundary value conditions via computational results”, Adv. Differ. Equ. 2020, Article No. 218 (2020), 1-40, https://doi.org/10.1186/s13662-020-02679-w.
  8. Etemad, S., Souid, M.S., Telli, B., Kaabar, M.K.A., and Rezapour, S., ”Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique”, Adv. Differ. Equ. 2021, Article No. 214 (2021), 1-20, https://doi.org/10.1186/s13662-021-03377-x.
  9. Gupta, V., Deep, R., ”Some coupled fixed point theorems in partially ordered S-metric spaces”, Miskols mathematical notes, 16:1 (2015), 181-194.
  10. Kamran, T., ”Coincidence and fixed points for hybrid strict contractions”, J. Math. Anal. Appl., 2991 (2004), 235-241.
  11. Mohammadi, H., Rezapour, S., Etemad, S., and Baleanu, D., ”Two sequential fractional hybrid differential inclusions”, Adv. Differ. Equ. 2020, Article No. 385 (2020), 1-24, https://doi.org/10.1186/s13662-020-02850-3.
  12. Mojaradiafra, J., and Sabbaghan, M., ”Some new applications of S-metric spaces by weakly compatible pairs with limit property”, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math, 28:1, (2021), 1-13.
  13. Nyein, E.E., and Zaw, A.K., ”Quasi (s, r)-contractive multi-valued operators on b-metric space and related fixed point theorems”, J. Indones. Math. Soc. , 26:3, (2020), 393-402.
  14. Pourgholam, A., and Sabbaghan, M., ”SH-metric spaces and fixed point theorems for multivalued weak contraction mappings”, Mathematical science, 15:4, (2021), 377-385.
  15. Sedghi, S., and Shobe, N., ”Fixed point theorem in M-fuzzy metric spaces with property (E)”, Adv in fuzzy Math, 1:1, (2006), 55-65.
  16. Sedghi, S., Shobe, N., and Aliouche, A., ”A generalization of fixed point theorems in S-metric spaces”, Mat.Vesn, 64:3, (2012), 258-266.
  17. Sedghi, S., Shobkolaei, N., Shahraki, M., and Dosenovic, T., ”Common fixed point of four maps in S-metric spaces”, Mathematical Sciences, (2018), 137-143.
  18. Shrivastava, S., Daheriya, R., and Ughade, M., ”S-metric space, expanding mappings & fixed point theorems”, International journal of scientific and innovative mathematical research, (2006), 1-12.
  19. Yicheng, L., Jun, W., and Zhixiang, L., ”Common fixed points of single-valued and multivalued maps”, International Journal of mathematics and mathematical sciences, (2005), 3045-3055