Sang Og Kim

Approximation on the Quadratic Reciprocal Functional Equation

The quadratic reciprocal functional equation is introduced. The Ulam stability problem for an -quadratic reciprocal mapping between nonzero real numbers is solved. The Găvruţa stability for the quadratic reciprocal functional equations is established as well.

Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

We obtain the general solution of the generalized mixed additive and quadratic functional equation , is even; , is odd, for a positive integer . We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces when is an even positive integer or .

Approximate m-Lie homomorphisms and approximate Jordan m-Lie homomorphisms associated to a parametric additive functional equation

AbstractUsing fixed point method, we establish the Hyers-Ulam stability of m-Lie homomorphisms and Jordan m-Lie homomorphisms in m-Lie algebras associated to the following generalized Jensen functional equation ∑i=1mμf(xi)=12m[∑i=1mf(μmxi+∑j=1,i≠jmxj)+f(∑i=1mμxi)] for a fixed positive integer m with m ≥ 2.Mathematics Subject Classification (2010): Primary 17A42, 39B82, 39B52.