Related papers: On Bloch's Theorem and the contraction mapping pri…

The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The…

Arbitrary operator A on a Banach space X which is the generator of C_0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse…

In this paper we prove that if $f$ is a self-mapping of a nonempty subset $K$ of a normed space $X$ that satisfies some mild conditions, then the minimal displacement of large iterations $f^n$ always dominates that of $f$ along certain…

In this paper, we begin by constructing global linear maps on (n-2)-dimensional subspaces, derived from the local continuity of linear transformations among central sections of a convex body. Using these linear maps, we subsequently…

We present closed graph and open mapping theorems for $\wt{\C}$-linear maps acting between suitable classes of topological and locally convex topological $\wt{\C}$-modules. This is done by adaptation of De Wilde's theory of webbed spaces…

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

We obtain an anlogue of Wigner's classical theorem on symmetries for Banach spaces. The proof is based on a result from the theory of linear preservers. Moreover, we present two other Wigner-type results for finite dimensional linear spaces…

Using the technique of Fra\"iss\'e theory, for every constant $K\ge 1$ we consruct a universal object in the class of Banach spaces with normalized $K$-suppression unconditional Schauder bases.

In [3, Theorem 6.7B], the authors use the Main Theorems of Brauer to give a proof of Burnside's Normal $p$-complement Theorem. Unfortunately, the proof contains an error. We take this opportunity to give a proof along similar lines,…

A version of the Bessaga inverse of the Banach contraction principle for partial metric spaces is presented. Equivalence of that version and the continuum hypothesis is shown as well.

We prove the $1$-dimensional flat chain conjecture in any complete and quasiconvex metric space, namely that metric $1$-currents can be approximated in mass by normal $1$-currents. The proof relies on a new Banach space isomorphism theorem,…

We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.

According to a result due to B.T. Polyak, a mapping between Hilbert spaces, which is $C^{1,1}$ around a regular point, carries a ball centered at that point to a convex set, provided that the radius of the ball is small enough. The present…

The aim of this paper is to prove a counterpart of the Banach fixed point principle for mappings $f: \ell_\infty(X) \to X$, where $X$ is a metric space and $\ell_\infty(X)$ is the space of all bounded sequences of elements from~$X$. Our…

The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…

In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach…

Stimulated by recent problems in the theory of iterated function systems, we provide a variant of the Banach converse theorem for multivalued maps. In particular, we show that attractors of continuous multivalued maps in a metric space are…

We prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of…

We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson (1977) : "If a normed space $E$ does not contain any…

We introduce the concept of vector-valued holomorphic mappings on the complex unit disc that factor through a Hilbert space and state the main properties of the space formed by such Bloch mappings equipped with a natural norm:…