A generalized common fixed point of multi-valued maps in b-metric space
DOI:
https://doi.org/10.5269/bspm.51655Abstract
In this work we are interested to prove a general fixed point theorem for a pair of multi-valued mappings in b-metric spaces. The results in this paper generalize the results obtained in [19] and to obtain other particular results.
References
1. A. Aghajani, M. Abbas, J. R. Roshan, Common Fixed Point of Generalized Weak Contractive Mappings in Partially Ordered b-Metric Spaces, Math. Slovaca 64 (2014), No. 4, 941-960. https://doi.org/10.2478/s12175-014-0250-6
2. M. U. Ali, T. Kamran, M. Postolache, Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem. Nonlinear Anal. Modelling Control 22(2017), No. 1, 17-30. https://doi.org/10.15388/NA.2017.1.2
3. H. Aydi, M. Bota, E. Karapinar, E. Mitrovıc, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl, 2012, doi:10.1186/1687-1812-2012-88. https://doi.org/10.1186/1687-1812-2012-88
4. I. A. Bakhtin, The contraction mapping principle in almost metric spaces. 30. In Functional Analysis. Ul'yanovsk Gos. Ped. Inst., Ul'yanovsk; 1989:26-37.
5. M. Boriceanu, A. Petrusel, I. A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Int. J. Math. Stat., 6(2010), 65-76.
6. M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4(2009), 285-301.
7. M. Bota, A. Moln'ar, C. Varga, On Ekeland's variational principle in b−metric spaces, Fixed Point Theory, 12(2011), 21-28.
8. S. Czerwik, Nonlinear set valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fiz. Univ. Modena, 46(1998), 263-276.
9. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav, 1(1993), 5-11.
10. Z. M. Fadail, A. G. B. Ahmad, Coupled coincidence point and common coupled fixed point results in cone b-metric spaces, Fixed Point Theory Appl, (2013) 177, https://doi.org/10.1186/1687-1812-2013-177
11. H. Huang, S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl, (2013) 112. https://doi.org/10.1186/1687-1812-2013-112
12. N. Hussain, M.H. Shah, K K M mappings in cone b-metric spaces, Comput. Math. Appl., 62(2011), 1677-1684. https://doi.org/10.1016/j.camwa.2011.06.004
13. T. Kamran, M. Postolache, M U. Ali, Q. Kiran : Feng and Liu type F-contraction in b-metric spaces with application to integral equations. J. Math. Anal. 7(2016), No. 5, 18-27. https://doi.org/10.1186/s13663-015-0486-z
14. B. Marzouki, A. El Haddouchi, Generalized altering distances and fixed point for occasionally hybrid mapping. Fasciculi. Mathematici. 56 (2016), 111-120. https://doi.org/10.1515/fascmath-2016-0007
15. B. Marzouki, A. El Haddouchi, Common fixed point of multivalued maps. Nonliear Analysis and Differential Equations. 4 (2016), 1-7. https://doi.org/10.12988/nade.2016.5720
16. B. Marzouki, A. El Haddouchi, A common fixed point theorem in modular space. Nonliear Analysis and Differential Equations. 4 (2016), 219-223. https://doi.org/10.12988/nade.2016.629
17. B. Marzouki, A. El Haddouchi, A generalized fixed point theorem in G-metric space. Journal of Analysis and applications. Vol 17 N2(2019), 89 - 105.
18. Mehmet, Kir. Hukmi, Kiziltunc, On Some Well Known Fixed Point theorems in b−Metric Spaces, Turkish Journal of Analysis and Number Theory, 2013, Vol. 1, No. 1, 13-16. https://doi.org/10.12691/tjant-1-1-4
19. R. Miculescu, A. Mihail, New fixed point therems for set-valued contraction in b-metric spaces, J. Fixed point Theory Appl.(2017). https://doi.org/10.1007/s11784-016-0400-2
20. W. Shatanawi, A. Pitea, R. Lazovic, : Contraction conditions using compa-rison functions on b-metric spaces, Fixed Point Theory Appl. Art. No. 135 (2014). https://doi.org/10.1186/1687-1812-2014-135
21. W. Shatanawi, Fixed and common fixed point for mappings satisfying some nonlinear contractions in b−metric spaces. Journal of Mathematical Analysis, Volume 7 Issue 4(2016), 1-12.
2. M. U. Ali, T. Kamran, M. Postolache, Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem. Nonlinear Anal. Modelling Control 22(2017), No. 1, 17-30. https://doi.org/10.15388/NA.2017.1.2
3. H. Aydi, M. Bota, E. Karapinar, E. Mitrovıc, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl, 2012, doi:10.1186/1687-1812-2012-88. https://doi.org/10.1186/1687-1812-2012-88
4. I. A. Bakhtin, The contraction mapping principle in almost metric spaces. 30. In Functional Analysis. Ul'yanovsk Gos. Ped. Inst., Ul'yanovsk; 1989:26-37.
5. M. Boriceanu, A. Petrusel, I. A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Int. J. Math. Stat., 6(2010), 65-76.
6. M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4(2009), 285-301.
7. M. Bota, A. Moln'ar, C. Varga, On Ekeland's variational principle in b−metric spaces, Fixed Point Theory, 12(2011), 21-28.
8. S. Czerwik, Nonlinear set valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fiz. Univ. Modena, 46(1998), 263-276.
9. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav, 1(1993), 5-11.
10. Z. M. Fadail, A. G. B. Ahmad, Coupled coincidence point and common coupled fixed point results in cone b-metric spaces, Fixed Point Theory Appl, (2013) 177, https://doi.org/10.1186/1687-1812-2013-177
11. H. Huang, S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl, (2013) 112. https://doi.org/10.1186/1687-1812-2013-112
12. N. Hussain, M.H. Shah, K K M mappings in cone b-metric spaces, Comput. Math. Appl., 62(2011), 1677-1684. https://doi.org/10.1016/j.camwa.2011.06.004
13. T. Kamran, M. Postolache, M U. Ali, Q. Kiran : Feng and Liu type F-contraction in b-metric spaces with application to integral equations. J. Math. Anal. 7(2016), No. 5, 18-27. https://doi.org/10.1186/s13663-015-0486-z
14. B. Marzouki, A. El Haddouchi, Generalized altering distances and fixed point for occasionally hybrid mapping. Fasciculi. Mathematici. 56 (2016), 111-120. https://doi.org/10.1515/fascmath-2016-0007
15. B. Marzouki, A. El Haddouchi, Common fixed point of multivalued maps. Nonliear Analysis and Differential Equations. 4 (2016), 1-7. https://doi.org/10.12988/nade.2016.5720
16. B. Marzouki, A. El Haddouchi, A common fixed point theorem in modular space. Nonliear Analysis and Differential Equations. 4 (2016), 219-223. https://doi.org/10.12988/nade.2016.629
17. B. Marzouki, A. El Haddouchi, A generalized fixed point theorem in G-metric space. Journal of Analysis and applications. Vol 17 N2(2019), 89 - 105.
18. Mehmet, Kir. Hukmi, Kiziltunc, On Some Well Known Fixed Point theorems in b−Metric Spaces, Turkish Journal of Analysis and Number Theory, 2013, Vol. 1, No. 1, 13-16. https://doi.org/10.12691/tjant-1-1-4
19. R. Miculescu, A. Mihail, New fixed point therems for set-valued contraction in b-metric spaces, J. Fixed point Theory Appl.(2017). https://doi.org/10.1007/s11784-016-0400-2
20. W. Shatanawi, A. Pitea, R. Lazovic, : Contraction conditions using compa-rison functions on b-metric spaces, Fixed Point Theory Appl. Art. No. 135 (2014). https://doi.org/10.1186/1687-1812-2014-135
21. W. Shatanawi, Fixed and common fixed point for mappings satisfying some nonlinear contractions in b−metric spaces. Journal of Mathematical Analysis, Volume 7 Issue 4(2016), 1-12.
Downloads
Published
2022-12-21
Issue
Section
Research Articles
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
