International Journal of Nonlinear Analysis and Applications

Weak subsequential continuity in fuzzy metric spaces and application

Document Type : Research Paper

Authors

1 Operators theory and PDE Laboratory, Department of Mathematics, Faculty of Exact Sciences, University of El Oued, P.O.Box789, El-Oued 39000, Algeria

2 Department of Mathematics, Government Degree College Thatyur, Tehri Garhwal, Uttarakhand, India

3 Department of Mathematics, V. S. K. C. Government P. G. College Dakpathar, Dehradun (Uttrakhand), India

Abstract

Compatibility of type (E) and weak subsequential continuity is utilized in a fuzzy metric space for the existence of a common fixed point. Illustrations and an application are stated to elucidate our outcomes.

Keywords

[1] R. Bellman and E. S. Lee, Functional equations in dynamic programming, Aequ. Math. 17 (1978) 1–18.
[2] S. Beloul, Common fixed point theorems for weakly subsequentially continuous generalized contractions with aplications, Appl. Maths. E-Notes, 15 (2015) 173–186.
[3] S. Beloul, Common fixed point theorems for weakly subsequentially continuous mappings in fuzzy metric spaces
via implicit relation, TWMS J. App. Eng. Math. 8(1) (2018) 284–294.
[4] S. Beloul and A. Tomar, Integral type common fixed point theorems in modified intuitionistic fuzzy metric spaces,
Afrika Mat. 3 (2019) 1–16.
[5] Y. J. Cho, S. Sedghi and N. Shobe, Generalized fixed point theorems for Compatible mappings with some types in
fuzzy metric spaces, Chaos, Solitons Fract. 39 (2009) 2233–2244.
[6] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces,Fuzzy Sets and Systems, 90
(1997) 365–368.
[7] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975) 336–344.
[8] S. Manro, A. Tomar and B. E. Rhoades, Coincidence and common fixed point theorems in fuzzy metric spaces
using a Meir-Keeler Type contractive condition, Gazi Univ. J. Sci. 27(1) (2014) 669–678.
[9] S. Manro and A. Tomar, Common fixed point theorems using property (E.A.) and its variants involving quadratic
terms, Ann. Fuzzy Math. Inf. 7(3) (2014) 473–484.
[10] S. Manro and A. Tomar, Faintly compatible maps and existence of common fixed points in fuzzy metric space,
Ann. Fuzzy Math. Inf. 8(2) (2014) 223–230.
[11] S. N. Mishra, N. Sharma and S. L. Singh, Common fixed point of maps on fuzzy metric spaces, Internat. J. Math.
Math. Sci. 17 (1994) 253–258.[12] R. P. Pant, A common fixed point theorem under a new condition, Indian. J. Pure Appl. Math. 30(2) (1999)
147–152.
[13] R. Rana, R. C. Dimri and A. Tomar, Fixed point theorems in Fuzzy Metric spaces using implicit relations, Int. J.
Comp. Appl. 8(1) 2010 16–21.
[14] D. O’Regan and M. Abbas, Necessary and sufficient conditions for common fixed point theorems in fuzzy metric
space, Demonstr. Math. 42(4) (2009).
[15] M. R. Singh and Y. M. Singh, Compatible mappings of type (E) and common fixed point theorems of Meir-Keeler
type, Int. J. Math. Sci. Engg. Appl. 1(2) (2007) 299–315.
[16] S. L. Singh and A. Tomar, Weaker forms of commuting maps and existence of fixed points, J. Korea. Soc. Math.
Educ. ser. B: Pure Appl. Math. 10(3) (2003) 145–161.
[17] S. L. Singh and A. Tomar, Fixed point theorems in FM-spaces, J. Fuzzy Math. 12(4) (2004).
[18] A. Tomar and E. Karapinar, On variants of continuity and existence of fixed point via Meir-Keeler contractions
in MC-spaces, J. Adv. Math. Stud. 9(2) (2016) 348–359.
[19] A. Tomar, S. Upadhyay and R. Sharma, Existence of common fixed point in symmetric space with application,
Elect. J. Math. Anal. Appl. 7(1) (2019) 116–129.
[20] L. A. Zadeh, Fuzzy sets, Inf. Cont. 89 (1965) 338–353.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 1485-1496
  • Receive Date: 19 April 2020
  • Revise Date: 30 June 2020
  • Accept Date: 21 July 2020