Jae-Hyeong Bae

A functional equation having monomials as solutions

For each n=1,2,3, we obtain the general solution and the stability of the functional equation f(2x+y)+f(2x-y)=2^n^-^2[f(x+y)+f(x-y)+6f(x)]. And we obtain the general solution and the stability of the functional equation f(2x+y)+f(2x-y)+6f(y)=4[f(x+y)+f(x-y)+6f(x)]. Using the fixed point method, we prove the generalized Hyers-Ulam stability of these functional equations.

Approximate Behavior of Bi-Quadratic Mappings in Quasinormed Spaces

We obtain the generalized Hyers-Ulam stability of the bi-quadratic functional equation in quasinormed spaces.

A Multidimensional Functional Equation Having Quadratic Forms as Solutions

We obtain the general solution and the stability of the-variable quadratic functional equation The quadratic form is a solution of the given functional equation.

Stability of a Cauchy-Jensen Functional Equation in Quasi-Banach Spaces

We obtain the generalized Hyers-Ulam stability of the Cauchy-Jensen functional equation .

On the Asymptoticity Aspect of Hyers-Ulam Stability of Quadratic Mappings

We investigate the Hyers-Ulam stability of the quadratic functional equation on restricted domains. Applying these results, we study of an asymptotic behavior of these quadratic mappings.

Generalized Dunkl-Williams inequality in 2-inner product spaces

We consider the generalized Dunkl-Williams inequality in 2-normed spaces. Also, we give necessary and sufficient conditions for having the equality case in the strictly convex 2-normed space X.

A fixed-point approach to the stability of a functional equation on quadratic forms

AbstractUsing the fixed-point method, we prove the generalized Hyers-Ulam stability of the functional equationn f(x+y,z+w)+f(x-y,z-w)=2f(x,z)+2f(y,w).n The quadratic form f : ℝ × ℝ → ℝ given by f(x, y) = ax2 + bxy + cy2 is a solution of the above functional equation.

Stability of a 2-Dimensional Functional Equation in a Class of Vector Variable Functions

We prove the Hyers-Ulam stability of a 2-dimensional quadratic functional equation in a class of vector variable functions in Banach modules over a unital -algebra.

On the Ulam-Hyers stability of a quadratic functional equation

AbstractThe Ulam-Hyers stability problems of the following quadratic equationn r2fx+yr+r2fx-yr=2f(x)+2f(y),n where r is a nonzero rational number, shall be treated. The case r = 2 was introduced by J. M. Rassias in 1999. Furthermore, we prove the stability of the quadratic equation by using the fixed point method.2010 Mathematics Subject Classification: 39B22; 39B52; 39B72.

Generalized ulam-hyers stability of C*-Ternary algebra n-Homomorphisms for a functional equation

AbstractIn this article, we investigate the Ulam-Hyers stability of C*-ternary algebra n-homomorphisms for the functional equation:n n in C*-ternary algebras.2000 Mathematics Subject Classification: Primary 39B82; 46B03; 47Jxx.