Home Suzuki-type of common fixed point theorems in fuzzy metric spaces
Article
Licensed
Unlicensed Requires Authentication

Suzuki-type of common fixed point theorems in fuzzy metric spaces

  • Shaban Sedghi , Nabi Shobkolaei , Tatjana Došenović and Stojan Radenović EMAIL logo
Published/Copyright: March 31, 2018
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 68 Issue 2

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.

MSC 2010: Primary 54H25; Secondary 47H10
Keywords: fixed point; fuzzy metric space; t-norm; Suzuki-type fixed point

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-3-1-133-181Search 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/s1-37.1.74Search 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.2011.09.046Search 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)90162-7Search 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)00088-9Search in Google Scholar

[6] Hadžić O. Common fixed point theorems for families of mapping in complete metric space, Math. Japon. 29 (1984), 127–134.Search in Google Scholar

[7] Hadžić O.—Pap, E.: Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, 2001.10.1007/978-94-017-1560-7Search 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).10.1186/1687-1812-2012-126Search in Google Scholar

[9] Jungck, G.: Commuting mappings and fixed points, Amer Math. Monthly 83 (1976), 261–263.10.2307/2318216Search in Google Scholar

[10] Jungck, G.: Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771–779.10.1155/S0161171286000935Search 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/S0161171290000096Search in Google Scholar

[12] Kramosil, I.—Michalek, J.: Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326–344.Search 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.10.1155/2008/649749Search 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.Search 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.2007.08.064Search in Google Scholar

[16] Mishra, S. N.: Common fixed points of compatible mappings in PM-spaces, Math. Japonica 36 (1991), 283–289.Search 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)00305-1Search 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.2007.07.006Search in Google Scholar

[19] Nemytzki, V. V.: The fixed point method in analysis (Russian), Usp. Mat. Nauk, 1 (1936), 141–174.Search 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/s11533-009-0019-2Search in Google Scholar

[21] Popescu, O.: Fixed point theorem in metric spaces, Bull. Transilv. Univ. Braşov 150 (2008), 479–482.Search 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.Search 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.2003.09.007Search 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.Search 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.Search 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/S0002-9939-07-09055-7Search 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.2009.04.017Search 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.Search 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)00131-8Search in Google Scholar

[30] Xieping, D.: Common fixed point theorem of commuting mappings in PM-spaces, Kexue Tongbao 29 (1984), 147–150.Search in Google Scholar

Received: 2016-6-20
Accepted: 2016-10-19
Published Online: 2018-3-31
Published in Print: 2018-4-25

© 2018 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  2. On the family of functions with closure of graphs in the Mendez ideals
  4. The predicate completion of a partial information system
  6. On lattices of z-ideals of function rings
  8. Compactifications of partial frames via strongly regular ideals
  10. Lifting components in clean abelian ℓ-groups
  12. Invariance of nonatomic measures on effect algebras
  14. On the alexander dual of path ideals of cycle posets
  16. Generalized multiplicative derivations in 3-prime near rings
  18. Cleft extensions for quasi-entwining structures
  20. Groups with positive rank gradient and their actions
  22. Certain results on q-starlike and q-convex error functions
  24. Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
  26. Positive periodic solutions for singular high-order neutral functional differential equations
  28. A special class of functional equations
  30. Matrix mappings and general bounded linear operators on the space bv
  32. Skew-symmetric operators and reflexivity
  34. Derivatives of Hadamard type in vector optimization
  36. Cardinal functions of the hyperspace of convergent sequences
  38. Suzuki-type of common fixed point theorems in fuzzy metric spaces
  40. Second hankel determinat for certain analytic functions satisfying subordinate condition
https://doi.org/10.1515/ms-2017-0115
Keywords for this article
fixed point; fuzzy metric space; t-norm; Suzuki-type fixed point

Articles in the same Issue

  2. On the family of functions with closure of graphs in the Mendez ideals
  4. The predicate completion of a partial information system
  6. On lattices of z-ideals of function rings
  8. Compactifications of partial frames via strongly regular ideals
  10. Lifting components in clean abelian ℓ-groups
  12. Invariance of nonatomic measures on effect algebras
  14. On the alexander dual of path ideals of cycle posets
  16. Generalized multiplicative derivations in 3-prime near rings
  18. Cleft extensions for quasi-entwining structures
  20. Groups with positive rank gradient and their actions
  22. Certain results on q-starlike and q-convex error functions
  24. Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
  26. Positive periodic solutions for singular high-order neutral functional differential equations
  28. A special class of functional equations
  30. Matrix mappings and general bounded linear operators on the space bv
  32. Skew-symmetric operators and reflexivity
  34. Derivatives of Hadamard type in vector optimization
  36. Cardinal functions of the hyperspace of convergent sequences
  38. Suzuki-type of common fixed point theorems in fuzzy metric spaces
  40. Second hankel determinat for certain analytic functions satisfying subordinate condition
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 15.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0115/html
Scroll to top button