Related papers: Projections in normed linear spaces and sufficient…

Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a {\it sufficient enlargement} for $X$ if, for an arbitrary isometric…

Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a {\it sufficient enlargement} for $X$ if, for an arbitrary isometric…

The notion of ball convexity, considered in finite dimensional real Banach spaces, is a natural and useful extension of usual convexity; one replaces intersections of half-spaces by suitable intersections of balls. A subset $S$ of a normed…

Let $X$ be a Banach space with the unit ball $B(X)$ and $A\subset X$ be a convex origin-symmetric compact in $X$. Let $\mathrm{j}:X\rightarrow \widetilde{X}$ be an isometric extension of $X$. It is well-known that linear widths $\lambda…

We introduce the notion of strongly orthogonal set relative to an element in the sense of Birkhoff-James in a normed linear space to find a necessary and sufficient condition for an element $ x $ of the unit sphere $ S_{X}$ to be an exposed…

Let $X$ be a finite-dimensional normed space and let $Y \subseteq X$ be its proper linear subspace. The set of all minimal projections from $X$ to $Y$ is a convex subset of the space all linear operators from $X$ to $X$ and we can consider…

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence…

In a normed linear space X an element x is said to be orthogonal to another element y in the sense of Birkhoff-James, written as $ x \perp_{B}y, $ iff $ \| x \| \leq \| x + \lambda y \| $ for all scalars $ \lambda.$ We prove that a normed…

The general problem we address is to develop new methods in the study of projection constants of Banach spaces of multivariate polynomials. The relative projection constant $\boldsymbol{\lambda}(X,Y)$ of a subspace $X$ of a Banach $Y$ is…

The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…

In this paper known results of symmetric orthogonality, as introduced by G. Birkhoff, and non-expansive nearest point projections are extended from the linear to the metric setting. If the space has non-positive curvature in the sense…

The \emph{relative projection constant} $\lambda(Y, X)$ of normed spaces $Y \subset X$ is defined as $\lambda(Y, X) = \inf \{ ||P|| : P \in \mathcal{P}(X, Y) \}$, where $\mathcal{P}(X, Y)$ denotes the set of all continuous projections from…

Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…

It is proved that the projection constants of two- and three-dimensional spaces are bounded by $4/3$ and $(1+\sqrt 5)/2$, respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and…

A bounded subset of a normed linear space is said to be (diametrically) complete if it cannot be enlarged without increasing the diameter. A complete super set of a bounded set $K$ having the same diameter as $K$ is called a completion of…

We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…

Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…

It is known that if $M$ is a finite-dimensional Banach space, or a strictly convex space, or the space $\ell_1$, then every non-expansive bijection $F: B_M \to B_M$ is an isometry. We extend these results to non-expansive bijections $F: B_E…

A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the…

The main objective of this article is to provide an alternative approach to the central result of [Eldred, A. Anthony, Kirk, W. A., Veeramani, P., Proximal normal structure and relatively nonexpansive mappings, Studia Math., vol 171(3),…