DOI QR코드

DOI QR Code

𝜓-TYPE CONTRACTION AND JAGGI TYPE HYBRID CONTRACTION IN BIPOLAR METRIC SPACES

  • Jong Kyu Kim (Department of Mathematics Education, Kyungnam University) ;
  • Manoj Kumar (Department of Mathematics, Baba Mastnath University) ;
  • Pankaj (Department of Mathematics, Baba Mastnath University)
  • Received : 2022.11.17
  • Accepted : 2023.01.18
  • Published : 2023.09.15

Abstract

In this paper, we will introduce the notion of 𝜓-type and Jaggi type hybrid contraction in a bipolar metric space and show the existence and uniqueness of fixed point for such type of contractions. In the end, we will provide some corollaries and support our theorems by examples.

Keywords

References

  1. S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux quations integrals, Fundam. Math., 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  2. M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc., 12 (1961), 7-10. https://doi.org/10.1090/S0002-9939-1961-0120625-6
  3. M.M. Fr'echet, Sur quelques points du culcul fonctionnel, Rendiconti del Circolo Matematico di Palermo, 22(1) (1906), 1-72. https://doi.org/10.1007/BF03018603
  4. D.S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math., 8(2) (1977), 223-230.
  5. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
  6. E. Karapinar and A. Fulga, A hybrid contraction that involves Jaggi type, Symmetry, 5 (2019), 715.
  7. J.K. Kim, M. Kumar and Pankaj, ω-Interpolative contractions in bipolar metric spaces, Nonlinear Funct Anal. Appl., 28(2) (2023), 383-394.
  8. D. Kitkuan, A. Padcharoen, J.K. Kim and W.H. Lim, On α-Geraghty contractive mappings in bipolar metric spaces, Nonlinear Funct Anal. Appl., 28(1) (2023), 295-309.
  9. A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969), 326-329. https://doi.org/10.1016/0022-247X(69)90031-6
  10. Z. Mustafa and B. Sims, A new aprroach to generalized metric spaces, J. Nonlinear Convex Anal., 7(2) (2006), 289-297.
  11. A. Mutlu and U. Gurdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl., 9 (2016), 5362-5373. https://doi.org/10.22436/jnsa.009.09.05
  12. A. Mutlu, U. Gurdal and K. Ozkan, Fixed point results for α - ψ-contractive mappings in bipolar metric spaces, J. Ineq. Special Funct., 11 (2020), 64-75.
  13. A. Mutlu, U. Gurdal and K. Ozkan, Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory, 21(1) (2020), 271-280. https://doi.org/10.24193/fpt-ro.2020.1.19
  14. B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear. Anal., 72(12) (2010), 4508-4517. https://doi.org/10.1016/j.na.2010.02.026
  15. B. Samet, Fixed points for α - ψ-contractive mappings with an application to quadratic integral equations, Elec. J. Diff. Equa., 152 (2014), 1-18.
  16. B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α - ψ-contractive type mappings, Nonlinear Anal., 75(4) (2012), 2154-2162. https://doi.org/10.1016/j.na.2011.10.014