A NEW TYPE OF THE ADDITIVE FUNCTIONAL EQUATIONS ON INTUITIONISTIC FUZZY NORMED SPACES |
Arunkumar, Mohan
(Department of Mathematics Government Arts College)
Bodaghi, Abasalt (Young Researchers and Elite Club Islamshahr Branch Islamic Azad University) Namachivayam, Thirumal (Department of Mathematics Government Arts College) Sathya, Elumalai (Department of Mathematics Government Arts College) |
1 | J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge Univ, Press, 1989. |
2 | T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950), 64-66. DOI |
3 | M. Arunkumar and T. Namachivayam, Intuitionistic fuzzy stability of a n-dimensional cubic functional equation: Direct and fixed point methods, Intern. J. Fuzzy Math. Arch. 7 (2015), 1-11. |
4 | K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), no. 1, 87-96. DOI |
5 | I. Beg, M. A. Ahmed, and H. A. Nafadi, Common fixed point theorems for hybrid pairs of L-fuzzy and crisp mappings in non-Archimedean fuzzy metric spaces, J. Nonlinear Funct. Anal. 2016 (2016), Article ID 35. |
6 | I. Beg, V. Gupta, and A. Kanwar, Fixed points on intuitionistic fuzzy metric spaces using the E.A. property, J. Nonlinear Funct. Anal. 2015 (2015), Article ID 20. |
7 | A. Bodaghi, Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations, J. Intel. Fuzzy Syst. 30 (2016), 2309-2317. DOI |
8 | A. Bodaghi, S. M. Moosavi, and H. Rahimi, The generalized cubic functional equation and the stability of cubic Jordan *-derivations, Ann. Univ. Ferrara Sez. VII Sci. Mat. 59 (2013), no. 2, 235-250. DOI |
9 | A. Bodaghi, Cubic derivations on Banach algebras, Acta Math. Vietnam. 38 (2013), no. 4, 517-528. DOI |
10 | A. Bodaghi, I. A. Alias, and M. Eshaghi Gordji, On the stability of quadratic double centralizers and quadratic multipliers: A fixed point approach, J. Inequal. Appl. 2011 (2011), Art ID 957541, 9 pages. DOI |
11 | A. Bodaghi, C. Park, and J. M. Rassias, Fundamental stabilities of the nonic functional equation in intuitionistic fuzzy normed spaces, Commun. Korean Math. Soc. 31 (2016), no. 4, 729-743. DOI |
12 | L. Cadariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timisoara Ser. Mat.-Inform. 41 (2003), no. 1, 25-48. |
13 | L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: A fixed point approach, Iteration theory (ECIT '02), 43-52, Grazer Math. Ber., 346, Karl-Franzens-Univ. Graz, Graz, 2004. |
14 | P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436. DOI |
15 | D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224. DOI |
16 | D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998. |
17 | S. A. Mohiuddine and Q. M. Danish Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos Solitons Fractals 42 (2009), no. 3, 731-1737. DOI |
18 | Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer Monographs in Mathematics, 2009. |
19 | S. O. Kim, A. Bodaghi, and C. Park, Stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces, J. Nonlinear Sci. Appl. 8 (2015), no. 5, 776-786. DOI |
20 | B. Margolis and J. B. Diaz, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 126 (1968), 305-309. |
21 | M. Mursaleen and S. A. Mohiuddine, On stability of a cubic functional equation in intuitionistic fuzzy normed spaces, Chaos Solitons Fractals 42 (2009), no. 5, 2997-3005. DOI |
22 | P. Narasimman and A. Bodaghi, Solution and stability of a mixed type functional equation, Filomat 31 (2017), no. 5, 1229-1239. DOI |
23 | J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 22 (2004), no. 5, 1039-1046. DOI |
24 | J. M. Rassias, On approximately of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), no. 1, 126-130. DOI |
25 | Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300. DOI |
26 | Th. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Acedamic Publishers, Dordrecht, Bostan London, 2003. |
27 | L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353. DOI |
28 | R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals 27 (2006), no. 2, 331-344. DOI |
29 | R. Saadati, S. Sedghi, and N. Shobe, Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos Solitons Fractals 38 (2008), no. 1, 36-47. DOI |
30 | S. Y. Yang, A. Bodaghi, and K. A. Mohd Atan, Approximate cubic *-derivations on Banach *-algebras, Abstr. Appl. Anal. 2012 (2012), Art ID 684179, 12 pp. |
31 | S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964. |