Abstract
In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation)
for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.
We obtain a general solution of the sextic functional equation f (ax+by)+ f
(ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)]
+ 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of
sextic Lie *-derivations associated with the given functional equation via
fixed point method. Also, we present a counterexample for a single case.
AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.
We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equationf(x+2y)+f(x−2y)=4(f(x+y)+f(x−y))−24f(y)−6f(x)+3f(2y)in quasi-Banach spaces.
We obtain the general solution of the generalized mixed additive and quadratic functional equationfx+my+fx−my=2fx−2m2fy+m2f2y,mis even;fx+y+fx−y−2m2−1fy+m2−1f2y,mis odd, for a positive integerm. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces whenmis an even positive integer orm=3.
Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces
