Recently added articles from Tamsui Oxford Journal of Mathematical Sciences:
On ([psi], [gamma])--stability of quadratic equation on groups.
Dec 15, 2008; ... 1. Introduction In 1940 to the audience of the Mathematics Club of the University of Wisconsin S. M. Ulam presented a list of unsolved problems (20). One of these problems can be considered as the starting point of a new line of investigations: the stability problem. The problem ...
On the isometric extension problem: a survey.
Dec 15, 2008; ... 1 Isometric extension problem Recall that if (E, [d.sub.E]) and (F, [d.sub.F]) are metric spaces then a mapping V from E into F is said to be an isometry if [d.sub.F](V[x.sub.1],V[x.sub.2]) = [d.sub.E]([x.sub.1], [x.sub.2]) for all [x.sub.1], [x.sub.2][member of]E. ...
On the stability of orthogonal functional equations.
Dec 15, 2008; ... 1. Introduction and preliminaries Assume that X is a real inner product space and f : X [right arrow] R is a solution of the orthogonal Cauchy functional equation f(x + y) = f(x) + f(y), [??]x,y[??] = 0. By the Pythagorean theorem f(x) = [||x||.sup.2] is a solution of the ...
Hyers-Ulam-Rassias stability of the Apollonius type quadratic mapping in non--Archimedean spaces.
Dec 15, 2008; ... 1. Introduction The stability problem of functional equations originated from a question of S.M. Ulam (25) concerning the stability of group homomorphisms: Let [G.sub.1] be a group and let [G.sub.2] be a metric group with the metric d(., .). Given [epsilon] > 0, does there exist ...
On the Hyers-Ulam stability of a system of Euler differential equations of first order.
Dec 15, 2008; ... 1. Introduction Assume that X is a normed space over a scalar field K and that I is an open interval, where K denotes either R or C. Let [a.sub.0], [a.sub.1], ..., [a.sub.n]: I [right arrow] K be given continuous functions, let g: I [right arrow] X be a given continuous ...