It is shown that if f is a mapping of the plane onto itself that is uniformly continuous with modulus of continuity (r) which is o(p r) as r ! 0 and f is also co-uniformly continuous then f = P h where h is a homeomorphism of the plane and P is a complex polynomial. The same conclusion holds also under other assumptions on the moduli of uniform and co-uniform continuity. However, we also presen...

The Haar and the Walsh functions are proved to be computable with respect to the Fine-metric dF which is induced from the in-nite product = {0; 1}{1;2; :::} with the weighted product metric dC of the discrete metric on {0; 1}. Although they are discontinuous functions on [0; 1] with respect to the Euclidean metric, they are continuous functions on ( ; dC) and on ([0; 1]; dF). On ( ; dC), comput...

in this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. then we investigate for a ring $r$, when any fi...

We prove that the flow map of the Kadomtsev-Petviashvili-I (KP-I) equation is not uniformly continuous on bounded sets of the natural energy space.

Many optimization problems can be reformulated as best approximation problems with respect to an appropriate norm. Their solutions are thus given by projection operators. It follows that projection operators play a key role in several areas, such as mechanics, minimization algorithms, variational inequalities, complementary problems. Thus, it is of interest to study the properties of such opera...

Abstract We consider a quasilinear degenerate parabolic equation driven by the orthotropic p -Laplacian. prove that local weak solutions are locally Lipschitz continuous in spatial variable, uniformly time.