Fuzzy Fixed Point Theorem for Multivalued \(F\)-Contraction in \(b\)-Metric Spaces

Darunee Hunwisai, Poom Kumam


In this work, we introduce and suggest the new concept of multivalued fuzzy \(F\)-contraction mappings in \(b\)-metric spaces. We also establish and prove the existence of an \(\alpha\)-fuzzy fixed point theorem in $b$-metric spaces.


\(b\)-metric space; Fuzzy mappings; Fuzzy fixed point; \(F\)-contraction

Full Text:



H.M. Abu-Donia, Common fixed point theorems for fuzzy mappings in metrics space under $phi$-contraction condition, Chaos Solitons Fractals 44 (2007), 538–543.

R.P. Agarwal, D.O. O’Regan and N. Shahzad, Fixed point theorem for generalized contractive maps of Meir-Keeler type, Mathematische Nachrichten 276 (2004), 3–22.

I. Altun, G. Minak and H. Dag, Multivalued F-contractions on complete metric spaces, Journal of Nonlinear and Convex Analysis 16 (4) (2015), 659–666.

A. Azam, M. Arshad and I. Beg, Fixed point of fuzzy contractive and fuzzy locally contractive maps, Chaos Solitons Fractals 42 (2009), 2836–2841.

I.A. Bakhtin, The contraction mapping principle in quasi-metric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26–37.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math. 3 (1922), 133–181.

T.G. Bhaskar and V. Lakshmikantham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal., Theory Methods Appl. 65 (2006), 1379–1393.

M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two bmetrics, Studia Univ Babes, Bolya: Math. LIV (3) (1989), 1–14.

M. Boriceanu, M. Bota and A. Petru, Multivalued fractals in b-metrics, Central European J. Math. 8 (2010), 367–377.

A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, International Journal of Mathematical and Mathematical Sciences 29 (2002), 531–536.

D. Butnariu, Fixed points for fuzzy mappings, Fuzzy Sets and Systems 7 (1982), 191–207.

S. Czerwik, Contraction mapping in b-metrics, Acta Mathematica et Informatica Universitatis Ostraviensis 1 (1993), 5–11.

S. Czerwik, Nonlinear set-valued contraction mappings in b-metrics, Atti Sem. Mat. Univ. Modena 46 (1998), 263–276.

S. Czerwik, K. Dlutek and S.L. Singh, Round-off stability of iteration procedures for operator in b-metrics, J. Natur. Phys. Sci. 11 (1997), 87–94.

V.D. Estruch and A. Vidal, A note on fixed fuzzy point for fuzzy mappings, Rend Ist. Mat. Univ. Trieste 32 (2001), 39–45.

Y. Feng and S. Liu, Fixed point theorem for multi-valued mappings and multi-valued Caristi type mapping, Journal of Mathematical Analysis and Application 317 (2006), 103–112.

S. Heilpern, Fuzzy mappings and fixed point theorem, Journal for Mathematical Analysis and Application 83 (1981), 566–569.

A. Ishak, M. Gülhan and D. Hacer, Multivalued F-contractions on complete metric spaces, Journal of Nonlinear and Convex Anlysis 16 (2015), 659–666.

E. Karapinar, M.A. Ksutbi, H. Piri and D. O’Regan, Fixed points of conditionally F-contractions in complete metric-like spaces, Journal of Nonlinear and Convex Anlysis 16 (2015), 659–666.

D. Klim and D. Wardowski, Fixed points of dynamic processes of set-valued F-contractions and application to functional equations, Fixed Point Theory and Applications 22 (2015), 9 p.

S.B. Nadler, Jr., Multivalued contraction mappings, Pacific Journal of Mathematicals 30 (1969), 475–488.

A. Padcharoen, D. Gopal, P. Chaipunya and P. Kumam, Fixed point and periodic point results for $alpha$-type F-contractions in modular metric spaces, Fixed Point Theory and Applications 39 (2016), 12 p.

S. Phiangsungnoen and P. Kumam, Fuzzy fixed point theorem for multivalued fuzzy contractions in b-metric spaces, J. Nonlinear Sci. Appl. 8 (2015), 55–63.

D. Turkoglu and B.E. Rhoades, A fixed fuzzy point for fuzzy mapping in complete metrics spaces, Fixed Point Theory Appl. 94 (2012), 6 p.

D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012), 6 p.

D. Wardowski and N.V. Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math. 1 (2014), 146–155.

L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338–353.


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905