Choonkil Park

Functional Inequalities Associated with Jordan-von Neumann-Type Additive Functional Equations

We prove the generalized Hyers‐Ulam stability of the following functional inequalities:,, in the spirit of the Rassias stability approach for approximately homomorphisms.

Non-Archimedean L-fuzzy normed spaces and stability of functional equations

Lee et al. considered the following quadratic functional equation f(lx+y)+f(lx-y)=2l^2f(x)+2f(y) and proved the Hyers-Ulam-Rassias stability of the above functional equation in classical Banach spaces. In this paper, we prove the Hyers-Ulam-Rassias stability of the above quadratic functional equation in non-Archimedean L-fuzzy normed spaces.

Fuzzy stability of a functional equation associated with inner product spaces

Moslehian et al. investigated the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces. In this paper, we prove the generalized Hyers-Ulam stability of a functional equation associated with inner product spaces in fuzzy Banach spaces.

Stability of an Additive-Cubic-Quartic Functional Equation

In this paper, we consider the additive-cubic-quartic functional equation and prove the generalized Hyers-Ulam stability of the additive-cubic-quartic functional equation in Banach spaces.

On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces

We establish the general solution of the functional equation for fixed integers with and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

Functional inequalities in non-Archimedean Banach spaces

Abstract In this work, we prove the generalized Hyers–Ulam stability of the following functional inequality: ‖ f ( x ) + f ( y ) + f ( z ) ‖ ≤ ‖ k f ( x + y + z k ) ‖ , | k | | 3 | , in non-Archimedean Banach spaces.

Homomorphisms and Derivations in

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in C*-algebras, Lie C*-algebras, and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras, and JC*-algebras associated with the following Apollonius-type additive functional equation f(z−x)

C^*

We obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary -norms .

-Algebras

The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ theorem was generalized by Aoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Rassias 4 has provided a lot of influence in the development of what we call generalized Hyers-Ulam stability or as Hyers-Ulam-Rassias stability of functional equations. A generalization of the Rassias theorem was obtained by Găvruţa 5 by replacing the unbounded Cauchy difference by a general control function in the spirit of Rassias’ approach. The functional equation

Quadratic-quartic functional equations in RN-spaces.

We prove the generalized stability of C*-ternary quadratic mappings in C*-ternary rings for the quadratic functional equation f(x