한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제31권3호
  • /
  • Pages.299-310
  • /
  • 2024
  • /
  • 1226-0657(pISSN)
  • /
  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지
DOI QR코드

DOI QR Code

SOME COMMON FIXED POINT THEOREMS WITH CONVERSE COMMUTING MAPPINGS IN BICOMPLEX-VALUED PROBABILISTIC METRIC SPACE

  • 투고 : 2024.04.04
  • 심사 : 2024.05.26
  • 발행 : 2024.08.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The probabilistic metric space as one of the important generalizations of metric space, was introduced by Menger [16] in 1942. Later, Choi et al. [6] initiated the notion of bicomplex-valued metric spaces (bi-CVMS). Recently, Bhattacharyya et al. [3] linked the concept of bicomplex-valued metric spaces and menger spaces, and initiated menger space with bicomplex-valued metric. Here, in this paper, we have taken probabilistic metric space with bicomplex-valued metric, i.e., bicomplexvalued probabilistic metric space and proved some common fixed point theorems using converse commuting mappings in this space.

키워드

과제정보

The authors are very much thankful to the reviewers for their valuable suggestions to bring the paper in its present form.

참고문헌

  1. A. Azam, F. Brain & M. Khan: Common fixed point theorems in complex valued metric spaces. Numer. Funct. Anal. Optim. 32 (2011), no. 3, 243-253. https://doi.org/10.1080/01630563.2011.533046
  2. R. Agarwal, M.P. Goswami & R.P. Agarwal: Bicomplex version of Stieltjes transform and applications. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 21 (2014), 229-246.
  3. S. Bhattacharyya, C. Biswas & T. Biswas: Common fixed point theorems in connection with two weakly compatible mappings in menger space with bicomplex-valued metric. Electron. J. Math. Anal. Appl. 12, (2024), no. (1, 9), 1-10. https://doi.org/10.21608/EJMAA.2024.243997.1087
  4. S. Chauhan & H. Sahper: Common fixed point theorems for conversely commuting mappings using implicit relations. J. Oper. Hindawi 2013, Article ID 391474, 5 pages. https://doi.org/10.1155/2013/391474
  5. S. Chauhan & B.D. Pant: Fixed points of weakly compatible mappings using common (E.A) like property. Matematiche 68 (2013) no. 1, 99-116.
  6. J. Choi, S.K. Datta, T. Biswas & Md N. Islam: Some fixed point theorems in connection with two weakly compatible mappings in bicomplex valued metric spaces. Honam Math. J. 39 (2017), no. 1, 115-126. https://doi.org/10.5831/HMJ.2017.39.1.115
  7. A.J. Gnanaprakasam, S.M. Boulaaras, G. Mani, B. Cherif & S.A. Idris: Solving system of linear equations via bicomplex valued metric space. Demonstr. Math. 54 (2021), 474-487. https://doi.org/10.1515/dema-2021-0046
  8. Md N. Islam: Fixed point theorems based on well-posedness and periodic point property in ordered bicomplex valued metric spaces. Malaya J. Mat. 9 (2020), no. 1, 9-19. https://doi.org/10.26637/MJM0901/0002
  9. G. Jungck: Compatible mappings and common fixed points. Int. J. Math. Math. Sci. 9 (1986), no. 4, 771-779. https://doi.org/10.1155/S0161171286000935
  10. G. Jungck & B.E. Rhoades: Fixed points for set valued functions without continuity. Indian J. Pure Appl. Math. 29 (1998), no. 3, 227-238.
  11. M.V.R. Kameswari & A. Bharathi: Common fixed points for a pair of maps in bicomplex valued generalized metric spaces. Adv. Appl. Math. Sci. 21 (2022), no. 5, 2345-2370.
  12. J. Kumar, R. Sharma & A. Singh: Common fixed point theorem for converse commuting maps in complex valued metric spaces. Int. J. Math. Archive 5 (2014), no. 6, 215-220.
  13. R.G. Lavoie, L. Marchildon & D. Rochon: In finite-dimensional bicomplex Hilbert spaces. Ann. Funct. Anal. 1 (2010), no. 2, 75-91. https://doi.org/10.15352/afa/1399900590
  14. Z.X. Lu: Common fixed points for converse commuting selfmaps on a metric space. Acta Anal. Funct. Appl. 4 (2002), no. 3, 226-228 (Chinese).
  15. G. Mani, A.J. Gnanaprakasam, R. George & G.D. Mitrovic: The existence of a solution of a nonlinear Fredholm integral equations over bicomplex b-metric spaces. Gulf J. Math. 14 (2023), no. 1, 69-83. https://doi.org/10.56947/gjom.v14i1.984
  16. K. Menger: Statistical metrics. Proc. Nat. Acad. Sci., U.S.A. 28 (1942), 535-537. https://doi.org/10.1073/pnas.28.12.535
  17. H.K. Pathak & R.K. Verma: Integral type contractive condition for converse commuting mappings. Int. J. Math. Anal. 3 (2009), no. 24, 1183-1190.
  18. H.K. Pathak & R.K. Verma: An Integral type implicit relation for converse commuting mappings. Int. J. Math. Anal. 3 (2009), no. 24, 1191-1198.
  19. V. Popa: A general fixed point theorem for converse commuting multi-valued mappings in symmetric spaces. Filomat 21 (2007), no. 2, 267-271.
  20. D. Rochon & M. Shapiro: On algebraic properties of bicomplex and hyperbolic numbers. An. Univ. Oradea Fasc. Mat. 11 (2004), 71-110.
  21. C. Segre: Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici. Math. Ann. 40 (1892), 413-467. https://doi.org/10.1007/BF01443559
  22. B. Schweizer & A. Sklar: Probabilistic metric spaces. North-Holland, Amsterdam, The Netherlands, 1983.
  23. R. Vasuki: Common fixed points for R-weakly commuting maps in fuzzy metric spaces. Indian J. Pure Appl. Math. 30 (1999), 419-423.