Se-Hyun Ku

A Mazur-Ulam problem in non-Archimedean n-normed spaces

In this article, we study the notions of n-isometries in non-Archimedean n-normed spaces over linear ordered non-Archimedean fields and prove the Mazur-Ulam theorem in the spaces. Furthermore, we obtain some properties for n-isometries in non-Archimedean n-normed spaces.MSC:46B20, 51M25, 46S10.

On stabilities of functional envelopes and its applications

Let (X, f) be a dynamical system and its functional envelope, where f is continuous. We prove the stabilities of the functional envelope defined by for any . And we also obtain some results for the derivations of function spaces.

A note on envelopes of homotopies

In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.