Abstract
In this article, by using a fixed point method, we establish the intuitionistic fuzzy version of Hyers-Ulam stability for a heptic functional equation that was introduced by Xu and Rassias. This way shows that the concept of stability is related to some fixed point of a suitable operator.
Keywords
- Heptic functional equation,
- Hyers-Ulam stability,
- Intuitionistic fuzzy normed space
References
- M. Arunkumar, A. Bodaghi, T. Namachivayam and E. Sathya, A new type of the additive functional equations on intuitionistic fuzzy normed spaces, Commun. Korean Math. Soc., 32(4)(2017), 915-932.
- T. Bag and S. K. Samanta, Some fixed point theorems on fuzzy normed linear spaces, Info Sci., 177(2007), 3271-3289.
- T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets Syst., 151(2005), 513-547.
- A. Bodaghi, Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations, J. Intel. Fuzzy Syst., 30(2016), 2309-2317.
- 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), Article ID
- A. Bodaghi, I. A. Alias and M. H. Ghahramani, Ulam stability of a quartic functional equation, Abs. Appl. Anal., 2012(2012), Art. ID
- A. Bodaghi, S. M. Moosavi and H. Rahimi, The generalized cubic functional equation and the stability of cubic Jordan *-derivations, Ann. Univ. Ferrara., 59(2013), 235-250.
- 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(4)(2016), 729-743.
- L. C˘adariu and V. Radu, Fixed points and stability for functional equations in probabilistic metric and random normed spaces, Fixed Point Theory Appl., 2009(2009), Article ID 589143,1 8 pages.
- L. C˘adariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timi¸soara, Ser. Mat. Inf., 41(2003), 25-48.
- L. C˘adariu and V. Radu, On the stability of the Cauchy functional equation: A fixed point approach, Grazer Math. Ber., 346(2004), 43-52.
- J. B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74(1968), 305-309.
- J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets Syst., 157(2006), 2739-2750.
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27(1941), 222-224.
- M. Eshaghi Gordji and A. Bodaghi,On the Hyers-Ulam-Rassias stability problem for quadratic functional equations, East J. App., 16(2)(2010), 123-130.
- M. Eshaghi Gordji, A. Bodaghi and C. Park, A fixed point approach to the stability of double Jordan centralizers and Jordan multipliers on Banach algebras, U.P.B. Sci. Bull., Series A., 73(2)(2011), 65-73.
- S. A. Mohiuddine and H. Sevli, Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space, J. Comp. Appl. Math., 235(2011), 2137-214.
- M. Mursaleen and S. A. Mohiuddine, On stability of a cubic functional equation in intuitionistic fuzzy normed spaces, Chaos, Solitons Fract., 42(2009), 2997-3005.
- M. Mursaleen and Q. M. D. Lohani, Intuitionistic fuzzy 2-normed space and some related concepts, Chaos, Solitons Fract., 42(2009), 224-234.
- J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons Fract., 22(2004), 1039-1046.
- R. Saadati, A note on some results on the IF-normed spaces, Chaos, Solitons Fract., 41(2009), 206-213.
- R. Saadati, Y. J. Cho and J. Vahidi, The stability of the quartic functional equation in various spaces, Comp. Math. Appl., 60(2010), 1994-2002.
- R. Saadati and C. Park, Non-archimedean L-fuzzy normed spaces and stability of functional equations, Comp. Math. Appl., 60(2010), 2488-2496.
- R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons Fract., 27(2006), 331-344.
- R. Saadati, A. Razani and H. Adibi, A common fixed point theorem in L-fuzzy metric spaces, Chaos, Solitons Fract., 33(2007), 354-363.
- R. Saadati, S. Sedghi and N. Shobe, Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos, Solitons Fract., 38(2008), 36-47.
- S. M. Ulam, Problems in modern mathematics, Chapter VI, Science Ed., Wiley, New York,
- T. Z. Xu, J. M. Rassias and W. X. Xu, A generalized mixed quadratic-quartic functional equation, Bull. Malay. Math. Sci. Soc., 35(3)(2012), 633-649.
- T. Z. Xu, M. J. Rassias and W. X. Xu, Stability of a general mixed additive-cubic functional equation in non-archimedean fuzzy normed spaces, J. Math. Phys., 51(2010), 093508, 19 pages.
- T. Z. Xu and J. M. Rassias, Approximate septic and octic mappings in quasi-β-normed spaces, J. Comp. Anal. Appl., 15(6)(2013), 1110-1119.
- T. Z. Xu, M. J. Rassias, W. X. Xu and J. M. Rassias, A fixed point approach to the intuitionistic fuzzy stability of quintic and sextic functional equations, Iran. J. Fuzzy Syst., 9(5)(2012), 21-
- L. A. Zadeh, Fuzzy sets, Inf. Cont., 8(1965), 338-353.
10.30495/maca.2021.1926769.1006