Some fixed point results for fuzzy generalizations of Nadler's contraction in b-metric spaces

Shazia Kanwal; Abdullah Al Mazrooei; Gustavo Santos-Garcia; Muhammad Gulzar; Shazia Kanwal; Abdullah Al Mazrooei; Gustavo Santos-Garcia; Muhammad Gulzar

doi:10.3934/math.2023515

AIMS Mathematics

2023, Volume 8, Issue 5: 10177-10195. doi: 10.3934/math.2023515

Previous Article Next Article

Research article Special Issues

Some fixed point results for fuzzy generalizations of Nadler's contraction in b-metric spaces

1.
Department of Mathematics, Government College University Faisalabad, Pakistan
2.
Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 80203, Saudi Arabia
3.
IME, Universidad de Salamanca, Spain

Received: 08 October 2022 Revised: 27 November 2022 Accepted: 07 December 2022 Published: 24 February 2023
MSC : 46S40, 47H10, 54H25

The main purpose of this study is to examine the existence of fuzzy fixed points of fuzzy mappings meeting the criteria of some generalized contractions of Nadler's type in the framework of complete b-metric spaces. From the pertinent literature, there are additional previous observations that are provided as corollaries. Our study expands and incorporates several implications that are apparent in this mode and are addressed in considerable literature.
- Nadler's contraction,
- fuzzy sets,
- fuzzy fixed point,
- fuzzy mapping,
- Hausdorff metric space
Citation: Shazia Kanwal, Abdullah Al Mazrooei, Gustavo Santos-Garcia, Muhammad Gulzar. Some fixed point results for fuzzy generalizations of Nadler's contraction in b-metric spaces[J]. AIMS Mathematics, 2023, 8(5): 10177-10195. doi: 10.3934/math.2023515

Related Papers:

Abstract

The main purpose of this study is to examine the existence of fuzzy fixed points of fuzzy mappings meeting the criteria of some generalized contractions of Nadler's type in the framework of complete b-metric spaces. From the pertinent literature, there are additional previous observations that are provided as corollaries. Our study expands and incorporates several implications that are apparent in this mode and are addressed in considerable literature.

References

[1]	S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations integrals, Fund. Math., 3 (1922), 133–181. https://doi.org/10.4064/fm-3-1-133-181 doi: 10.4064/fm-3-1-133-181
[2]	S. B. Nadler, Multi-valued contraction mappings, Pac. J. Math., 30 (1969), 475–488. https://doi.org/10.2140/pjm.1969.30.475 doi: 10.2140/pjm.1969.30.475
[3]	J. V. Neumann, Zur theorie der gesellschaftsspiele, Math. Ann., 100 (1928), 295–320. https://doi.org/10.1007/BF01448847 doi: 10.1007/BF01448847
[4]	M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Creat. Math. Inform., 3 (2009), 1–14. https://doi.org/10.1186/s13663-015-0350-1 doi: 10.1186/s13663-015-0350-1
[5]	S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263–276.
[6]	M. De la Sen, A. F. Roldán, R. P. Agarwal, On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points, Fixed Point Theory A., 2015 (2015), 103.
[7]	M. S. Abdullahi, A. Azam, L-fuzzy fixed point theorems for L-fuzzy mappings satisfying rational inequality, Thai J. Math., 19 (2021), 529–541.
[8]	M. Arshad, A. Shoaib, Fixed points of multivalued mappings in fuzzy metric spaces, In Proceedings of the World Congress on Engineering, 1 (2012), 4–6.
[9]	S. Kanwal, A. Azam, Bounded lattice fuzzy coincidence theorems with applications, J. Intell. Fuzzy Syst., 36 (2019), 1–15, https://doi.org/10.3233/JIFS-181754 doi: 10.3233/JIFS-181754
[10]	A. Tassaddiq, S. Kanwal, S. Perveen, R. Srivastava, Fixed points of singlevalued and multi-valued mappings in sb-metric spaces, J. Inequal. Appl., 2022 (2022). https://doi.org/10.1186/s13660-022-02814-z
[11]	L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
[12]	S. Heilpern, Fuzzy mappings and fixed point theorem, J. Math. Anal. Appl., 83 (1981), 566–569. https://doi.org/10.1016/0022-247X(81)90141-4 doi: 10.1016/0022-247X(81)90141-4
[13]	M. D. Weiss, Fixed points, separation, and induced topologies for fuzzy sets, J. Math. Anal. Appl., 50 (1975), 142–150. https://doi.org/10.1016/0022-247X(75)90044-X doi: 10.1016/0022-247X(75)90044-X
[14]	D. Butnariu, Fixed points for fuzzy mappings, Fuzzy Set. Syst., 7 (1982), 191–207. https://doi.org/10.1016/0165-0114(82)90049-5 doi: 10.1016/0165-0114(82)90049-5
[15]	I. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., 30 (1989), 26–37.
[16]	S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5–11.
[17]	A. Azam, Fuzzy fixed points of fuzzy mappings via a rational inequality, Hacet. J. Math. Stat., 40 (2011), 421–431.
[18]	S. Kanwal, U. Hanif, M. E. Noorwali, M. A. Alam, Existence of α_L-fuzzy fixed points of L-fuzzy mappings, Math. Probl. Eng., 2022 (2022), 1–10. https://doi.org/10.1155/2022/6878428. doi: 10.1155/2022/6878428
[19]	A. Azam, S. Kanwal, Common fixed point results for multivalued mappings in Hausdorff intuitionistic fuzzy metric spaces, Commun. Math. Appl., 9 (2018), 63–75.
[20]	S. Kanwal, A. Azam, Common fixed points of intuitionistic fuzzy maps for Meir-Keeler type contractions, Adv. Fuzzy Syst., 2018 (2018), 1989423. https://doi.org/10.1155/2018/1989423 doi: 10.1155/2018/1989423
[21]	Z. Mustafa, V. Parvaneh, J. R. Roshan, Z. Kadelburg, b_2_Metric spaces and some fixed point theorems, Fixed Point Theory A., 144 (2014). https://doi.org/10.1186/1687-1812-2014-144
[22]	J. R. Roshan, N. Shobkolaei, S. Sedghi, V. Parvaneh, S. Radenovic, Common fixed point theorems for three maps in discontinuous G_b metric spaces, Acta Math. Sci., 34 (2014), 1643–1654. https://doi.org/10.1016/S0252-9602(14)60110-7 doi: 10.1016/S0252-9602(14)60110-7
[23]	N. Hussain, J. R. Roshan, V. Parvaneh, A. Latif, A unification of G-metric, partial metric, and b-metric spaces, Abstr. Appl. Anal., 2014 (2014), 180698. https://doi.org/10.1155/2014/180698. doi: 10.1155/2014/180698
[24]	S. Phiangsungnoen, P. Kumam, Fuzzy fixed point theorems for multivalued fuzzy contractions in b-metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 55–63. https://doi.org/10.22436/jnsa.008.01.07 doi: 10.22436/jnsa.008.01.07
[25]	S. Phiangsungnoen, W. Sintunavarat, P. Kumam, Common α-fuzzy fixed point theorems for fuzzy mappings via $\beta_F$-admissible pair, J. Intell. Fuzzy Syst., 27 (2014), 2463–2472. https://doi.org/10.3233/IFS-141218 doi: 10.3233/IFS-141218
[26]	Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Fixed point theorems for weakly T-Chatterjea and weakly T-Kannan contractions in b-metric spaces, J. Inequal. Appl., 2014 (2014). https://doi.org/10.1186/1029-242X-2014-46 doi: 10.1186/1029-242X-2014-46
[27]	D. M. Zoran, V. Parvaneh, N. Mlaiki, N. Hussain, S. Radenović, On some new generalizations of Nadler contraction in b-metric spaces, Cogent Math. Stat., 7 (2020), 1760189. https://doi.org/10.1080/25742558.2020.1760189 doi: 10.1080/25742558.2020.1760189
[28]	R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theor. Appl., 19 (2017), 2153–2163. https://doi.org/10.1007/s11784-016-0400-2 doi: 10.1007/s11784-016-0400-2
[29]	L. B. Ciric, Generalized contractions and fixed-point theorems. Publ. Inst. Math., 12 (1971), 19–26.
[30]	S. Kanwal, M. S. Shagari, H. Aydi, A. Mukheimer, T. Abdeljawad, Common fixed-point results of fuzzy mappings and applications on stochastic Volterra integral equations, J. Inequal. Appl., 110 (2022). https://doi.org/10.1186/s13660-022-02849-2. doi: 10.1186/s13660-022-02849-2

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)