Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

COMMON FIXED POINT RESULTS VIA F-CONTRACTION ON C* -ALGEBRA VALUED METRIC SPACES

  • Shivani Kukreti (Department of Mathematics, H.N.B. Garhwal University) ;
  • Gopi Prasad (Department of Mathematics, Dr. Shivanand Nautiyal Goverment Post Graduate College) ;
  • Ramesh Chandra Dimri (Department of Mathematics, H.N.B. Garhwal University)
  • Received : 2023.09.17
  • Accepted : 2023.11.09
  • Published : 2023.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this work, we establish common fixed point results by utilizing a variant of F-contraction in the framework of C*-algebra valued metric spaces. We utilize E.A. and C.L.R. property possessed by the mappings to prove common fixed point results in the same metric settings. To validate the applicability of these common fixed point results, we provide illustrative examples too.

Keywords

Acknowledgement

The referees have reviewed the paper very carefully. The authors express their deep thanks for the comments.

References

  1. S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  2. S.G. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728 (1994 ), 183-197. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x
  3. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Univ. Ostrav. 1 (1993), 5-11.
  4. A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. 57 (2000), 31-37.
  5. M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416-420. https://doi.org/10.1016/j.jmaa.2007.09.070
  6. J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Am. Math. Soc. 136 (4), (2008), 1359-1373. https://doi.org/10.1090/S0002-9939-07-09110-1
  7. Y. J. Cho, R. Saadati, S. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl., 61 (2011), 1254-1260. https://doi.org/10.1016/j.camwa.2011.01.004
  8. R.C. Dimri, G. Prasad, Coincidence theorems for comparable generalized non-linear contractions in ordered partial metric spaces, Commun. Korean Math. Soc. 32 (2) (2017), 375-387. https://doi.org/10.4134/CKMS.c160127
  9. G. Prasad, Fixed point theorems via w-distance in relational metric spaces with an application, Filomat 34(6) (2020), 1889-1898. https://doi.org/10.2298/FIL2006889P
  10. G. Prasad, R.C. Dimri, A. Bartwal, Fixed points of Suzuki contractive mappings in relational metric spaces, Rend. Circ. Mat. Palermo, Ser II 69 (2020), 1347-1358. https://doi.org/10.1007/s12215-019-00475-4
  11. G. Prasad, D. Khantwal, Fixed points of JS-contractive mappings with applications, J. Anal. 31 (4) (2023), 2687-2701. https://doi.org/10.1007/s41478-023-00598-z
  12. D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012,94, (2012).
  13. D. Wardwoski, N. V. Dung, Fixed points of F-weak contraction on complete metric spaces, Demonstr. Math. 47 (2014).
  14. D. Klim, D. Wardowski, Fixed points of dynamic processes of set-valued F contractions and application to functional equations, Fixed Point Theory Appl. 2015, 22, (2015).
  15. I. Altun, G. Minak, H. Dag, Multivalued F-contractions on complete metric spaces, J. Nonlinear Convex Anal. 16 (2015), 659-666.
  16. M. Nazam, C. Park, A. Hussain, M. Arshad, J. R. Lee, Fixed point theorems for F-contractions on closed ball in partial metric spaces, J. Comput. Anal. Appl. 27 (2019), 759-769.
  17. Z.H. Ma, L.N. Jiang, H.K. Sun, C∗-algebra valued metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2014, 206, (2014).
  18. Z.H. Ma, L.N. Jiang, C∗-algebra valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2015, 222, (2015). https://doi.org/10.1186/s13663-015-0471-6
  19. M.E. Ege, C. C. Alaca, C∗-algebra-valued S-metric spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 67 (2) (2018), 165-177. https://doi.org/10.1501/Commua1_0000000871
  20. N. Mlaike, M. Asim, M. Imdad, C∗-algebra valued partial b-metric spaces and fixed point results with an application, Mathematics 8 (8), (2020). https://doi.org/10.3390/math8081381
  21. J.U. Maheswari, A. Anbarasan, M. Gunaseelan, V. Parvaneh, H. Bonab, Solving an integral equation via C∗-algebra-valued partial b-metrics, Fixed Point Theory Algorithms Sci Eng 2022, 18 (2022).
  22. W. Tapanyo, W. Ratiphaphongthon, A. Arunchai, Completion of C∗-algebra-valued metric spaces, Thai J. Math., 20 (3), (2022), 1119-1136.
  23. G. Mani, A.J. Gnanaprakasam, O. Ege, A. Aloqaily, N. Mlaiki, Fixed point results in C∗-algebravalued partial b-metric spaces with related application, Mathematics 11 (5), 1158, (2023) 1-9. https://doi.org/10.3390/math11051158
  24. M. Paul, K. Sarkar, K. Tiwary, Some unique common fixed point results on C∗-algebra valued metric space using C∗-class function, Ann. Math. Comput. Sci. 16, (2023), 1-20.
  25. S. Narzary, D. Das, Y.M. Singh, M.S. Khan, S. Sessa, C∗-algebra-valued partial modular metric spaces and some fixed point results, Symmetry 15 (6) (2023), 1135.
  26. X. Qiaoling, J. Lining, Z. Ma, Common fixed point theorems in C∗-algebra valued metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 4617-4627. https://doi.org/10.22436/jnsa.009.06.100
  27. D. El. Moutawakil, M. Aamri, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), 181-188. https://doi.org/10.1016/S0022-247X(02)00059-8
  28. P. Kumam, W. Sintunavarat, Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space, J. Appl. Math. 2011 (2011). https://doi.org/10.1155/2011/637958
  29. K. Goebel, A coincidence theorem, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 16 (1968), 733-735.
  30. G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (3), (1998), 227-238.