Abstract
The modular fuzzy b-metric space is defined in this study, and we are interested in proving a general common fixed point theorem for a pair of multi-valued mappings in Hausdorff modular fuzzy b-metric spaces. The work generalizes the findings in [H. Kerim, W. Shatanawi, A. Tallafha and T. A. M. Shatnawi, Fixed point theorems on modular fuzzy metric spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 84 2022, 1, 47–58] and produce additional specific findings that are supported by examples. An application to prove the existence of an integral inclusion equation’s solution is shown to demonstrate the importance of our result.
Acknowledgements
The authors would like to thank the referee sincerely for very helpful comments improving the paper.
References
[1] I. A. Bakhtin, The contraction mapping principle in almost metric space, Funct. Anal. Gos. Ped. Inst. Unianowsk 30 (1989), 26–37. Suche in Google Scholar
[2] M. Boriceanu, A. Petruşel and I. A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Int. J. Math. Stat. 6 (2010), no. S10, 65–76. Suche in Google Scholar
[3] M. Bota, A. Molnár and C. Varga, On Ekeland’s variational principle in b-metric spaces, Fixed Point Theory 12 (2011), no. 1, 21–28. Suche in Google Scholar
[4] V. V. Chistyakov, Modular metric spaces generated by F-modulars, Folia Math. 15 (2008), no. 1, 3–24. Suche in Google Scholar
[5] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11. Suche in Google Scholar
[6] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena 46 (1998), no. 2, 263–276. Suche in Google Scholar
[7] M. Dahhouch, N. Makran and B. Marzouki, A common fixed point of multivalued maps in extended b-metric space with application Volterra-type integral inclusion, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 84 (2022), no. 4, 139–148. Suche in Google Scholar
[8] T. Došenović, A. Javaheri, S. Sedghi and N. Shobe, Coupled fixed point theorem in b-fuzzy metric spaces, Novi Sad J. Math. 47 (2017), no. 1, 77–88. 10.30755/NSJOM.04361Suche in Google Scholar
[9] M. E. Ege and C. Alaca, Some results for modular b-metric spaces and an application to system of linear equations, Azerb. J. Math. 8 (2018), no. 1, 3–14. Suche in Google Scholar
[10] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), no. 3, 395–399. 10.1016/0165-0114(94)90162-7Suche in Google Scholar
[11] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems 90 (1997), no. 3, 365–368. 10.1016/S0165-0114(96)00207-2Suche in Google Scholar
[12] Z. Hassanzadeh and S. Sedghi, Relation between b-metric and fuzzy metric spaces, Math. Morav. 22 (2018), no. 1, 55–63. 10.5937/MatMor1801055HSuche in Google Scholar
[13] S. Heilpern, Fuzzy mappings and fixed point theorem, J. Math. Anal. Appl. 83 (1981), no. 2, 566–569. 10.1016/0022-247X(81)90141-4Suche in Google Scholar
[14] H. Kerim, W. Shatanawi, A. Tallafha and T. A. M. Shatnawi, Fixed point theorems on modular fuzzy metric spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 84 (2022), no. 1, 47–58. Suche in Google Scholar
[15] I. Kramosil and J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), no. 5, 336–344. Suche in Google Scholar
[16] N. Makran, A. El Haddouchi and B. Marzouki, A common fixed point of multi-valued maps in b-metric space, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 82 (2020), no. 1, 197–206. Suche in Google Scholar
[17]
N. Makran, A. El Haddouchi and B. Marzouki,
A generalized common fixed points for multivalued mappings in
[18] N. Makran, A. El Haddouchi and B. Marzouki, A generalized common fixed point of multi-valued maps in b-metric space, Bol. Soc. Parana. Mat. (3) 41 (2023), 9. 10.5269/bspm.51655Suche in Google Scholar
[19] L. Maligranda, Orlicz Spaces and Interpolation, Semin. Math. 5, Universidade Estadual de Campinas, Campinas, 1989. Suche in Google Scholar
[20] B. Marzouki, N. Makran and A. El Haddouchi, A generalized common fixed point theorem in complex valued b-metric spaces, Bol. Soc. Parana. Mat. (3) 40 (2022), 1–9. 10.5269/bspm.51616Suche in Google Scholar
[21] J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18 (1959), 49–65. 10.4064/sm-18-1-49-65Suche in Google Scholar
[22] J. Musielak and W. Orlicz, Some remarks on modular spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 (1959), 661–668. Suche in Google Scholar
[23] H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen, Tokyo, 1950. Suche in Google Scholar
[24] D. Rakić, A. Mukheimer, T. Došenović, Z. D. Mitrović and S. Radenović, On some new fixed point results in fuzzy b-metric spaces, J. Inequal. Appl. 2020 (2020), Paper No. 99. 10.1186/s13660-020-02371-3Suche in Google Scholar
[25] S. Sedghi, M. S. Khan, N. Shobe and S. Sedghi, Common fixed point theorems in fuzzy metric spaces, Nonlinear Funct. Anal. Appl. 14 (2009), no. 3, 349–355. 10.1155/2009/546273Suche in Google Scholar
[26] S. Sedghi and N. Shobe, Common fixed point theorem for R-weakly commuting maps in b-fuzzy metric space, Nonlinear Funct. Anal. Appl. 19 (2014), no. 2, 285–295. Suche in Google Scholar
[27] L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338–353. 10.1016/S0019-9958(65)90241-XSuche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Chern flat, Chern–Ricci flat twisted product in almost Hermitian geometry
- A study of Horn matrix functions and Horn confluent matrix functions
- A common fixed point result for multi-valued mappings in Hausdorff modular fuzzy b-metric spaces with application to integral inclusions
- (L p,λ,μ,L q,λ,μ) boundedness of the G-fractional integral operator on G-Morrey spaces
- Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function
- Analysis of the beta-logarithmic function and its properties
- Regarding the set-theoretic complexity of the general fractal dimensions and measures maps
Artikel in diesem Heft
- Frontmatter
- Chern flat, Chern–Ricci flat twisted product in almost Hermitian geometry
- A study of Horn matrix functions and Horn confluent matrix functions
- A common fixed point result for multi-valued mappings in Hausdorff modular fuzzy b-metric spaces with application to integral inclusions
- (L p,λ,μ,L q,λ,μ) boundedness of the G-fractional integral operator on G-Morrey spaces
- Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function
- Analysis of the beta-logarithmic function and its properties
- Regarding the set-theoretic complexity of the general fractal dimensions and measures maps