Suzuki-type of common fixed point theorems in fuzzy metric spaces
-
Shaban Sedghi
Abstract
In this paper by using of Suzuki-type approach we introduce the new contractive condition in the framework of non-Archimedean fuzzy metric spaces. We prove also the corresponding coincidence fixed point theorem for two mappings in this framework. Finally, two examples are presented to verify the effectiveness and applicability of our main results.
The third author is supported by MNTRRS-174009.
References
[1] Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.10.4064/fm-3-1-133-181Suche in Google Scholar
[2] Edelstein, M.: On fixed and periodic point under contractive mappings, J. Lond. Math. Soc. 37 (1962), 74–79.10.1112/jlms/s1-37.1.74Suche in Google Scholar
[3] Djorić D.—Kadelburg, Z.—Radenović S.: Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces, Nonlinear Anal. 75 (2012), 1927–1932.10.1016/j.na.2011.09.046Suche in Google Scholar
[4] George, A.—Veeramani, P.: On some result in fuzzy metric space, Fuzzy Sets and Systems 64 (1994), 395–399.10.1016/0165-0114(94)90162-7Suche in Google Scholar
[5] Gregori, V.—Sapena, A.: On fixed-point theorem in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), 245–252.10.1016/S0165-0114(00)00088-9Suche in Google Scholar
[6] Hadžić O. Common fixed point theorems for families of mapping in complete metric space, Math. Japon. 29 (1984), 127–134.Suche in Google Scholar
[7] Hadžić O.—Pap, E.: Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, 2001.10.1007/978-94-017-1560-7Suche in Google Scholar
[8] Hussain, N.— Djorić D., Kadelburg, Z., Radenović S.: Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl. 2012:126 (2012).10.1186/1687-1812-2012-126Suche in Google Scholar
[9] Jungck, G.: Commuting mappings and fixed points, Amer Math. Monthly 83 (1976), 261–263.10.2307/2318216Suche in Google Scholar
[10] Jungck, G.: Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771–779.10.1155/S0161171286000935Suche in Google Scholar
[11] Kang, S. M.—Cho, Y. J.—Jungck, G.: Common fixed point of compatible mappings, Int. J. Math. Math. Sci. 13 (1990), 61–66.10.1155/S0161171290000096Suche in Google Scholar
[12] Kramosil, I.—Michalek, J.: Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326–344.Suche in Google Scholar
[13] Kikkawa, M.—Suzuki, T.: Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl. 2008 (2008), Article ID 649749, 8 pp.10.1155/2008/649749Suche in Google Scholar
[14] Kikkawa, M.—Suzuki, T.: Some notes on Fixed point theorems with constants, Bull. Kyushu Inst. Technol. Pure Appl. Math. 56 (2009), 11–18.Suche in Google Scholar
[15] Kikkawa, M.—Suzuki, T.: Three Fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008), 2942–2949.10.1016/j.na.2007.08.064Suche in Google Scholar
[16] Mishra, S. N.: Common fixed points of compatible mappings in PM-spaces, Math. Japonica 36 (1991), 283–289.Suche in Google Scholar
[17] Miheţ D.: A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems 144 (2004), 431–439.10.1016/S0165-0114(03)00305-1Suche in Google Scholar
[18] Miheţ D.: Fuzzy ψ-contractive mappimgs in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159 (2008), 739–744.10.1016/j.fss.2007.07.006Suche in Google Scholar
[19] Nemytzki, V. V.: The fixed point method in analysis (Russian), Usp. Mat. Nauk, 1 (1936), 141–174.Suche in Google Scholar
[20] Popescu, O.: Two Fixed point theorems for generalized contractions with constants in complete metric space, Cent. Eur. J. Math. 7:3 (2009), 529–538.10.2478/s11533-009-0019-2Suche in Google Scholar
[21] Popescu, O.: Fixed point theorem in metric spaces, Bull. Transilv. Univ. Braşov 150 (2008), 479–482.Suche in Google Scholar
[22] Rhoades, B. E.: Common fixed point theorems for nonself Quasi-Contraction Mappings, Varohmihir Journal of Mathematical Sciences 2: I (2002), 11–14.Suche in Google Scholar
[23] Rodrígez López, J.—Romaguera, S.: The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems 147 (2004), 273–283.10.1016/j.fss.2003.09.007Suche in Google Scholar
[24] Sedghi, S.—Choudhury, B. S.—Shobe, N.: Unique common fixed point theorem for four weakly compatible mappings in complete fuzzy metric spaces, J. Fuzzy Math. 18 (2010), 161–170.Suche in Google Scholar
[25] Shobkolaei, N.—Sedghi, S.: Suzuki-type fixed point results for E-contractive maps in uniform spaces, Thai J. Math. 14(3) (2016), 575–583.Suche in Google Scholar
[26] Suzuki, T.: A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861–1869.10.1090/S0002-9939-07-09055-7Suche in Google Scholar
[27] Suzuki, T.: A new type of fixed point theorem in metric spaces, Nonlinear Anal. 71 (2009), 5313–5317.10.1016/j.na.2009.04.017Suche in Google Scholar
[28] Vasuki, R.: Common fixed points for R-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math. 30 (1999), 419–423.Suche in Google Scholar
[29] Vasuki, R.—Veeramani, P.: Fixed point theorems and Cauchy sequences in fuzzy metric spaces, Fuzzy Sets and Systems 135 (2003), 409–413.10.1016/S0165-0114(02)00131-8Suche in Google Scholar
[30] Xieping, D.: Common fixed point theorem of commuting mappings in PM-spaces, Kexue Tongbao 29 (1984), 147–150.Suche in Google Scholar
© 2018 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- On the family of functions with closure of graphs in the Mendez ideals
- The predicate completion of a partial information system
- On lattices of z-ideals of function rings
- Compactifications of partial frames via strongly regular ideals
- Lifting components in clean abelian ℓ-groups
- Invariance of nonatomic measures on effect algebras
- On the alexander dual of path ideals of cycle posets
- Generalized multiplicative derivations in 3-prime near rings
- Cleft extensions for quasi-entwining structures
- Groups with positive rank gradient and their actions
- Certain results on q-starlike and q-convex error functions
- Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
- Positive periodic solutions for singular high-order neutral functional differential equations
- A special class of functional equations
- Matrix mappings and general bounded linear operators on the space bv
- Skew-symmetric operators and reflexivity
- Derivatives of Hadamard type in vector optimization
- Cardinal functions of the hyperspace of convergent sequences
- Suzuki-type of common fixed point theorems in fuzzy metric spaces
- Second hankel determinat for certain analytic functions satisfying subordinate condition
Artikel in diesem Heft
- On the family of functions with closure of graphs in the Mendez ideals
- The predicate completion of a partial information system
- On lattices of z-ideals of function rings
- Compactifications of partial frames via strongly regular ideals
- Lifting components in clean abelian ℓ-groups
- Invariance of nonatomic measures on effect algebras
- On the alexander dual of path ideals of cycle posets
- Generalized multiplicative derivations in 3-prime near rings
- Cleft extensions for quasi-entwining structures
- Groups with positive rank gradient and their actions
- Certain results on q-starlike and q-convex error functions
- Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
- Positive periodic solutions for singular high-order neutral functional differential equations
- A special class of functional equations
- Matrix mappings and general bounded linear operators on the space bv
- Skew-symmetric operators and reflexivity
- Derivatives of Hadamard type in vector optimization
- Cardinal functions of the hyperspace of convergent sequences
- Suzuki-type of common fixed point theorems in fuzzy metric spaces
- Second hankel determinat for certain analytic functions satisfying subordinate condition
