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.
The aim of this paper is to give some new identities and relations related to
the some families of special numbers such as the Bernoulli numbers, the
Euler numbers, the Stirling numbers of the first and second kinds, the
central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?)
which are given Simsek [31]. Our method is related to the functional
equations of the generating functions and the fermionic and bosonic p-adic
Volkenborn integral on Zp. Finally, we give remarks and comments on our
results.
AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.
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.
Hyers-Ulam stability of quadratic forms in 2-normed spaces
