Solution and two types of Ulam-Hyers stability of $n-$ dimensional cubic-quartic functional equation in intuitionistic normed spaces
Authors :
John M. Rassias1, M. Arunkumar2, P. Agilan3*
Author Address :
1Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, Athens 15342,
Greece.
2Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
3Department of Mathematics, Jeppiaar Institute of Technology, Sriperumbudur, Chennai - 631 604, Tamil Nadu, India.
*Corresponding author.
Abstract :
In this paper, the authors investigate the generalized Ulam-Hyers stability of $n-$ dimensional cubic-quartic functional equation
egin{align*}
&fleft(sum_{b=1}^{n-1}v_b+rv_n ight)+fleft(sum_{b=1}^{n-1}v_b-rv_n ight)=r^2left[fleft(sum_{b=1}^{n}v_b ight)+fleft(sum_{b=1}^{n-1}v_b-v_n ight) ight] otag
&qquadqquad qquadqquadqquadqquadqquadqquad-2(r^2-1)fleft(sum_{b=1}^{n-1}v_b ight)+frac{2(r+1)}{r}left[f(rv_n)-r^3f(v_n) ight]
end{align*}
where $r$ is a positive integer with $r e pm 0,1$ in the setting of intuitionistic fuzzy normed spaces using direct and fixed point methods.
Keywords :
Cubic functional equation, quartic functional equation, generalized Ulam-Hyers stability, fixed point, intuitionistic fuzzy normed spaces.
DOI :
Article Info :
Received : October 11, 2017; Accepted : December 30, 2017.
