Related papers: Isometries on certain non-complete vector-valued f…

Not all convex functions on $\mathbb{R}^n$ have finite minimizers; some can only be minimized by a sequence as it heads to infinity. In this work, we aim to develop a theory for understanding such minimizers at infinity. We study astral…

We consider pairs of a non-empty compact connected and locally connected Hausdorff space and a real-valued continuous function. Our aim is to measure the difference between this kind of the pairs. In this notes we introduce new…

On a complete, connected, locally compact, non-compact geodesic space $(X,d)$, we assign each compact set a distance-like function. With the help of these functions, we obtain a pseudo-metric on the space of (non-empty) compact subsets of…

We prove that every TVS-cone metric space (i.e a cone metric space over a locally convex topological vector space $E$) is first countable paracompact topological space and by using Du's results in " [A note on cone metric fixed point theory…

Let $f: S(E) \to S(B)$ be a surjective isometry between the unit spheres of two weakly compact JB$^*$-triples not containing direct summands of rank smaller than or equal to 3. Suppose $E$ has rank greater than or equal to 5. Applying…

A vector topology on a vector space over a topological field is a (not necessarily Hausdorff) topology by which the addition and scalar multiplication are continuous. We prove that, if an isomorphism between the lattice of topologies of two…

We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…

In this paper, we establish two minimax theorems for functions $f:X\times I\to {\bf R}$, where $I$ is a real interval, without assuming that $f(x,\cdot)$ is quasi-concave. Also, some related applications are presented.

The Egoroff theorem for measurable $\bold X$-valued functions and operator-valued measures $\bold m: \Sigma \to L(\bold X, \bold Y)$, where $\Sigma$ is a $\sigma$-algebra of subsets of $T \neq \emptyset$ and $\bold X$, $\bold Y$ are both…

Let $E$ be one of the spaces $C(K)$ and $L_1$, $F$ be an arbitrary Banach space, $p>1,$ and $(X,\sigma)$ be a space with a finite measure. We prove that $E$ is isometric to a subspace of the Lebesgue-Bochner space $L_p(X;F)$ only if $E$ is…

The main result states that every convex set-valued function defined on a real interval with compact values in a locally convex space, admits an affine selection. In the case if the target space is a real line and the values are closed real…

We consider *-linear maps into a commutative C*-algebra C (X) of continuous functions on a locally compact Hausdorff space X with certain specified properties and prove two results: (1) an extension result for a class of *-linear maps Y -->…

We first prove a version of Tietze-Urysohn's theorem for proper functions taking values in non-negative real numbers defined on $\sigma$-compact locally compact Hausdorff spaces. As its application, we prove an extension theorem of proper…

For ordered normed vector spaces $X, Y$, we consider the space $\mathcal{L}(X,Y)$ of bounded linear operators and characterize when its cone of positive operators has non-empty interior. When this is satisfied, we give a functional…

We say that a (countably dimensional) topological vector space $X$ is orbital if there is $T\in L(X)$ and a vector $x\in X$ such that $X$ is the linear span of the orbit ${T^nx:n=0,1,...}$. We say that $X$ is strongly orbital if,…

Let $G$ be a group of homeomorphisms of a topological space $X$. $G$ is $\textit{(properly) isometrizable}$ if there exists a $G$-invariant (proper) gauge structure on $X$. $G$ is $\textit{equiregular}$ if for every $x \in X$ and every open…

Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\colon C\to\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate…

This work concerns the study of the subdifferential of the integral functional $$ E_f(x)=\int_{T} f(t,x)d\mu(t), $$ where $f$ is a (not necessarily convex) normal integrand, $({T},\mathcal{A},\mu)$ is a $\sigma$-finite measure space, while…

We investigate the existence of compact Hausdorff spaces $X$ that are minimum with respect to $cX=K$ for some fixed covering operator $c$ and compact Hausdorff space $K$ with $cK=K$. Then, using the Yosida representation theorem, we show…

Let E and F be Banach spaces, let A be a subset of E, and let s \ge 0. A map f: A -> F is an s-nearisometry if |x-y|-s \le |fx-fy| \le |x-y|+s for all x,y in A. The article gives a survey on the stability problem: How well can an…