Korean Journal of Mathematics

  • 제32권2호
  • /
  • Pages.245-257
  • /
  • 2024
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

EXPANSIVE TYPE MAPPINGS IN DISLOCATED QUASI-METRIC SPACE WITH SOME FIXED POINT RESULTS AND APPLICATION

  • Haripada Das (Department of Mathematics, Gauhati University) ;
  • Nilakshi Goswami (Department of Mathematics, Gauhati University)
  • 투고 : 2024.03.10
  • 심사 : 2024.05.11
  • 발행 : 2024.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we prove some new fixed point results for expansive type mappings in complete dislocated quasi-metric space. A common fixed point result is also established considering such mappings. Suitable examples are provided to demonstrate our results. The solution to a system of Fredholm integral equations is also established to show the applicability of our results.

키워드

참고문헌

  1. C. Aage and J. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci. 2 (59) (2008), 2941-2948.
  2. M. Ahmed, A common fixed point theorem for expansive mappings in 2-metric spaces and its application, Chaos, Solitons Fractals 42 (5) (2009), 2914-2920. https://doi.org/10.1016/j.chaos.2009.04.034
  3. S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1) (1922), 133-181.
  4. S. Cobzas, Fixed points and completeness in metric and generalized metric spaces, J. Math. Sci. 250 (2020), 475-535. https://doi.org/10.1007/s10958-020-05027-1
  5. R. Daheriya, R. Jain and M. Ughade, Some fixed point theorem for expansive type mapping in dislocated metric space, ISRN Math. Anal. 2012 (2012), Article ID 376832.
  6. B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math. 6 (12) (1975), 1455-1458.
  7. J. Gornicki, Fixed point theorems for F-expanding mappings, Fixed Point Theory Appl. 2017 (2017), Paper No 9. https://doi.org/10.1186/s13663-017-0602-3
  8. N. Goswami and B. Patir, Fixed-point theorems for (φ, ψ, β)-Geraghty contraction type mappings in partially ordered fuzzy metric spaces with applications, Korean J. Math. 30 (2) (2022), 375-389.
  9. Y. Han and S. Xu, Some new theorems of expanding mappings without continuity in cone metric spaces, Fixed Point Theory Appl. 2013 (2013), Paper No. 3. https://doi.org/10.1186/1687-1812-2013-3
  10. P. Hitzler and A. K. Seda, Dislocated topologies, J. Electr. Eng. 51 (12) (2000), 3-7.
  11. T. Hu, On a fixed-point theorem for metric spaces, Amer. Math. Monthly 74 (4) (1967), 436-437.
  12. U. M. Jeevanandam, A. Annadurai, G. Mani and S. Kumar, Some common fixed point theorem of rational contractive mappings in dislocated metric spaces, Topo. Alg. Appl. 11 (1) (2023), 20220135. https://doi.org/10.1515/taa-2022-0135
  13. S. Li, A. Zada, R. Shah and T. Li, Fixed point theorems in dislocated quasi-metric spaces, J. Nonlinear Sci. Appl. 10 (2017), 4695-4703. https://doi.org/10.22436/jnsa.010.09.12
  14. S. Matthews, Metric domains for completeness, PhD thesis, Department of Computer Science, University of Warwick Coventry, UK, 1-127, (1986).
  15. S. Mhanna, O. Baiz, H. Benaissa and D. El Moutawakil, Some new results of fixed point in dislocated quasi-metric spaces, J. Math. Comput. Sci. 24 (2022), 22-32. http://dx.doi.org/10.22436/jmcs.024.01.03
  16. M. Rahman and M. Sarwar, Fixed point theorems for expanding mappings in dislocated metric space, Math. Sci. Lett. 4 (1) (2015), 69-73. https://www.naturalspublishing.com/files/published/zy8r14l4g1nm54.pdf
  17. A. Rani, A. Rani and K. Jyoti, d - α - ψ expansive mapping in dislocated metric space, Asian J. Math. Comput. Research 15 (2) (2017), 103-112.
  18. B. Rhoades, A comparison of various definition of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290.
  19. B. Rhoades, Some fixed point theorems for pairs of mappings, Jnanabha 15 (1985), 151-156.
  20. P. Shahi, J. Kaur and S. Bhatia, Fixed point theorems for (ξ, α)-expansive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), Paper No. 157. https://doi.org/10.1186/1687-1812-2012-157
  21. T. Taniguchi, Common fixed point theorems on expansion type mappings on complete metric spaces, Math. Japon. 34 (1989), 139-142.
  22. S. Z. Wang, B.Y. Li, Z.M. Gao and K. Iseki, Some fixed point theorerms on expansion mappings, Math. Japon. 29 (1984), 631-636.
  23. S. S. Yesilkaya and C. Aydin, Fixed point results of expansive mappings in metric spaces, Math. 8 (10) (2020), Paper No. 1800. https://doi.org/10.3390/math8101800
  24. F. Zeyada, G. Hassan and M. Ahmed, A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces, Arab. J. Sci. Eng. 31 (1A) (2005), 111.