Geodesic
Fuzzy fixed point theorems for multivalued fuzzy contractions in $b$-metric spaces
Phiangsungnoen, Supak1 ; Kumam, Poom1
1 Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bang Mod, Thrung Kru, Bangkok 10140, Thailand;Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 1, p. 55-63.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we introduce the new concept of multivalued fuzzy contraction mappings in $b$-metric spaces and establish the existence of $\alpha$-fuzzy fixed point theorems in $b$-metric spaces which can be utilized to derive Nadler's fixed point theorem in the framework of b-metric spaces. Moreover, we provide examples to support our main result.
DOI : 10.22436/jnsa.008.01.07
Classification : 47H10, 54H25
Keywords: \(b\)-metric spaces, fuzzy fixed point, fuzzy mappings, fuzzy set.

Phiangsungnoen, Supak 1 ; Kumam, Poom 1

1 Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bang Mod, Thrung Kru, Bangkok 10140, Thailand;Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand 
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Phiangsungnoen, Supak; Kumam, Poom. Fuzzy fixed point theorems for multivalued fuzzy contractions in \(b\)-metric spaces. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 1, p. 55-63. doi : 10.22436/jnsa.008.01.07. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.01.07/

[1] Abbas, M.; Damjanović, B.; Lazović, R. Fuzzy common fixed point theorems for generalized contractive mappings, Appl. Math. Lett., Volume 23 (2010), pp. 1326-1330

[2] Ahmad, J.; Azam, A.; S. Romaguera On locally contractive fuzzy set valued mappings, J. Inequalities Appl., Volume 2014 (2014), pp. 1-10

[3] Aydi, H.; Bota, M-F.; Karapinar, E.; Mitrović, S. A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl, Volume 2012 (2012), pp. 1-8

[4] Aydi, H.; Bota, M-F.; Karapinar, E.; S. Moradi A common fixed point for weak -contractions on b-metric spaces, Fixed Point Theory, Volume 13 (2012), pp. 337-346

[5] Azam, A.; Arshad, M.; Beg, I. Fixed points of fuzzy contractive and fuzzy locally contractive maps, Chaos, Solitons and Fractals, Volume 4 (2009), pp. 2836-2841

[6] Azam, A.; Beg, I. Common fixed points of fuzzy maps, Mathematical and Computer Modelling, Volume 49 (2009), pp. 1331-1336

[7] Bakhtin, I. A. The contraction mapping principle in quasimetric spaces , Funct. Anal., Unianowsk Gos. Ped. Inst., Volume 30 (1989), pp. 26-37

[8] V. Berinde Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, Preprint, Volume 3 (1993), pp. 3-9

[9] Boriceanu, M.; Bota, M.; A.Petru Multivalued fractals in b-metric spaces , Central European J. Math., Volume 8 (2010), pp. 367-377

[10] Boriceanu, M.; Petruşel, A.; I. A. Rus Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Int. J. Math. Stat., Volume 6 (2010), pp. 65-76

[11] Boriceanu, M. Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., Volume 4 (2009), pp. 285-301

[12] M. Boriceanu Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. Babeş-Bolyai, Mathematica, Volume 3 (2009), pp. 3-14

[13] Bose, R. K.; Roychowdhury, M. K. Fixed point theorems for generalized weakly contractive mappings, Surv. Math. Appl., Volume 4 (2009), pp. 215-238

[14] Bota, M.; Karapnar, E.; O.Mleşniţe Ulam-Hyers stability results for fixed point problems via \(\alpha-\psi\) -contractive mapping in (b)-metric space, Abstract and Applied Analysis, Article ID 825293 , Volume 2013 (2013), pp. 1-6

[15] Czerwik, S. Contraction meppings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, Volume 1 (1993), pp. 5-11

[16] Czerwik, S.; Dlutek, K.; Singh, S. L. Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci., Volume 11 (1997), pp. 87-94

[17] Czerwik, S. Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, Volume 46 (1998), pp. 263-276

[18] Estruch, V. D.; A. Vidal A note on fixed fuzzy points for fuzzy mappings, Rend Istit Univ Trieste, Volume 32 (2001), pp. 39-45

[19] Frigon, M.; O'Regan, D. Fuzzy contractive maps and fuzzy fixed points, Fuzzy Sets and Systems, Volume 129 (2002), pp. 39-45

[20] Heilpern, S. Fuzzy mappings and fixed point theorems, J. Math. Anal. Appl., Volume 83 (1981), pp. 566-569

[21] Kutbi, M. A.; Ahmad, J.; Azam, A.; Hussain, N. On fuzzy fixed points for fuzzy maps with generalized weak property, J. Appl. Math., Article ID 549504, Volume 2014 (2014), pp. 1-12

[22] Kutbi, M. A.; Karapinar, E.; Ahmad, J.; Azam, A. Some fixed point results for multi-valued mappings in b-metric spaces, J. Inequalities Appl., Volume 2014 (2014), pp. 1-11

[23] Lee, B. S.; Cho, S. J. A fixed point theorem for contractive type fuzzy mappings, Fuzzy Sets and Systems, Volume 61 (1994), pp. 309-312

[24] S. B. Nadler Multivalued contraction mapping, Pacific J. Math., Volume 30 (1969), pp. 475-488

[25] J. von Neumann Zur theorie der gesellschaftsspiele, Math. Annalen, Volume 100 (1928), pp. 295-320

[26] Phiangsungnoen, S.; Sintunavarat, W.; Kumam, P. Common \(\alpha\)-fuzzy fixed point theorems for fuzzy mappings via \(\beta_ \mathcal{F}\)-admissible pair, J. Intelligent and Fuzzy Systems, Volume 27 (2014), pp. 2463-2472

[27] Phiangsungnoen, S.; Sintunavarat, W.; Kumam, P. Fuzzy fixed point theorems in Hausdorff fuzzy metric spaces, J. Inequalities Appl., Volume 2014 (2014), pp. 1-10

[28] Phiangsungnoen, S.; Sintunavarat, W.; Kumam, P. Fuzzy fixed point theorems for fuzzy mappings via \(\beta\)-admissible with applications, J. Uncertainty Anal, Appl, Volume 2 (2014), pp. 1-17

[29] Singh, B.; Chauhan, M. S. Fixed points of associated multimaps of fuzzy maps, Fuzzy Sets and Systems, Volume 110 (2000), pp. 131-134

[30] Singh, S. L.; Prasad, B. Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl., Volume 55 (2008), pp. 2512-2520

[31] Sintunavarat, W.; Plubtieng, S.; Katchang, P. Fixed point result and applications on b-metric space endowed with an arbitrary binary relation, Fixed Point Theory and Applications, Volume 2013 (2013), pp. 1-13

[32] Turkoglu, D.; Rhoades, B. E. A fixed fuzzy point for fuzzy mapping in complete metric spaces, Math. Commun., Volume 10 (2005), pp. 115-121

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