Related papers: Generalized projections on general Banach spaces
There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and…
In this paper, we introduced two new generalized metric spaces called partial b_{v}(s) and b_{v}({\theta}) metric spaces which extend b_{v}(s) metric space, b-metric space, rectangular metric space, v-generalized metric space, partial…
Non-trivial examples of generalized paracomplex structures (in the sense of the generalized geometry \`a la Hitchin) are constructed applying the twistor space construction scheme.
We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of $c_0$ and superreflexivity are discussed.
Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, we explore a pure algebraic…
Geometric quantiles are location parameters which extend classical univariate quantiles to normed spaces (possibly infinite-dimensional) and which include the geometric median as a special case. The infinite-dimensional setting is highly…
We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.
We focus on the new type perturbed metric spaces and introduce a contraction mapping namely new type perturbed Kannan mappings. For these mappings, we show that Banach's fixed point theorem holds. Moreover, this new generalization of…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
In this paper, we investigate a new notion of accretive mappings called generalized $\alpha\beta$-$H((.,.),(.,.))$-mixed accretive mappings in Banach spaces. We extend the concept of proximal-point mappings associated with generalized…
This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that…
In this paper, by using admissible sets, we give some fixed point results for orbitally contractions which diminish the radius of invariant convex subsets and orbits. Furthermore, a characterization of the weak normal structure by the fixed…
We present different extensions of the Banach contraction principle in the $G$-metric space setting. More precisely, we consider mappings for which the contractive condition is satisfied by a power of the mapping and for which the power…
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 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 $H$ be a real Hilbert space and $C$ a nonempty closed and convex subset of $H$. Let $P_C: H\rightarrow C$ denote the (standard) metric projection operator. In this paper, we study the G\^ateaux directional differentiability of $P_C$ and…
Generalized complex geometry, introduced by Hitchin, encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation…
We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…
We show that every metric space with bounded geometry uniformly embeds into an explicit reflexive Banach space (a direct sum of l^p spaces). In the case of discrete groups we show the analogue of a-T-menability. That is, we construct a…