Interpolation of Quasi-Normed Spaces.

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.

Stability Problems of Quintic Mappings in Quasi--Normed Spaces

Fixed points of Ćirić quasi-contractive operators in normed spaces

We establish a general theorem to approximate fixed points of Ćirić quasi-contractive operators on a normed space through the Mann iteration process with errors in the sense of Xu [10]. Our result generalizes and improves upon, among others, the corresponding results of [1,8].

Stability of the Monomial Functional Equation in Quasi Normed Spaces

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X → Y , which satisfies the inequality ||∆xf(y)− n!f(x)|| ≤ φ(x, y) for suitable control function φ, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of t 7→ f(tx) and t 7→ φ(tx, ty) imply the continuity of t 7→ M(tx).

Effortless quasi-interpolation in hierarchical spaces

We present a general and simple procedure to construct quasi-interpolants in hierarchical spaces, which are composed of a hierarchy of nested spaces. The hierarchical quasi-interpolants are described in terms of the truncated hierarchical basis. Once for each level in the hierarchy a quasi-interpolant is selected in the corresponding space, the hierarchical quasi-interpolants are obtained witho...