Complex interpolation for normed and quasi-normed spaces in several dimensions. III. Regularity results for harmonic interpolation

Quotients of Finite-dimensional Quasi-normed Spaces

We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to `∞ for some k. We give two results of this nature. The first guarantees a proportional dimensional cubic quotient when the envelope is cubic; the second gives an estimate for the size of a cubic quotient in terms of a measure of nonconvexity of the quasi-norm.

Saturating Constructions for Normed Spaces

We prove several results of the following type: given finite dimensional normed space V there exists another space X with log dimX = O(log dimV ) and such that every subspace (or quotient) of X, whose dimension is not “too small,” contains a further subspace isometric to V . This sheds new light on the structure of such large subspaces or quotients (resp., large sections or projections of conve...

SOME NEW RESULTS ON REMOTEST POINTS IN NORMED SPACES

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...

-approximation in normed spaces

APPROXIMATE FIXED POINT IN FUZZY NORMED SPACES FOR NONLINEAR MAPS

We de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.