Yang-Hi Lee

On an n-dimensional mixed type additive and quadratic functional equation

In this paper, we investigate the generalized Hyers-Ulam stability of the functional [emailxa0protected]?k2,...,kn=01fx[emailxa0protected]?i=2n(-1)^k^^ixi-2^n^-^1f(x1)-2^n^-^[emailxa0protected]?i=2nf(xi)+f(-xi)=0for integer values of n such that n>=2, where f is a function from a normed space X to a Banach space Y. The solutions of the equation are called additive-quadratic mappings.

Fuzzy stability of a mixed type functional equation

AbstractIn this paper, we investigate a fuzzy version of stability for the functional equationn f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0n in the sense of Mirmostafaee and Moslehian.1991 Mathematics Subject Classification. Primary 46S40; Secondary 39B52.

Fuzzy stability of a general quadratic functional equation

We investigate a fuzzy version of stability for the functional equation f (x + y + z) + f (x - y) + f (x - z) - f (x - y - z) - f (x + y) - f (x + z) = 0 in the sense of M. Mirmostafaee and M. S. Moslehian.

On the Stability of a New Pexider-Type Functional Equation

We establish the generalized Hyers-Ulam stability of a Pexider-type functonal equation , which is mixed of a quadratic and an additive functional equations. Also, we obtain its general solution from the stability results.

Hyers-Ulam Stability of a Bi-Jensen Functional Equation on a Punctured Domain

We obtain the Hyers-Ulam stability of a bi-Jensen functional equation: and simultaneously . And we get its stability on the punctured domain.

A general theorem on the stability of a class of functional equations including quadratic-additive functional equations

We prove a general stability theorem of an n-dimensional quadratic-additive type functional equation

Stability of a Bi-Jensen Functional Equation II

begin{aligned} Df(x_1, x_2, ldots , x_n) = sum _{i=1}^m c_i f big ( a_{i1}x_1 + a_{i2}x_2 + cdots + a_{in}x_n big ) = 0 end{aligned}

On a bi-Pexider functional equation and its stability

Df(x1,x2,…,xn)=∑i=1mcif(ai1x1+ai2x2+⋯+ainxn)=0by applying the direct method.