Related papers: On coupled best proximity points and Ulam-Hyers st…
Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order. Geometrically, they can be seen as a consequence of the (infinite dimensional) group of…
The purpose of this article is to study the anti-coproximinal and strongly anti-coproximinal subspaces of the Banach space of all bounded (continuous) functions. We obtain a tractable necessary condition for a subspace to be stronsgly…
We say that a metric space $(X,d)$ possesses the \emph{Banach Fixed Point Property (BFPP)} if every contraction $f:X\to X$ has a fixed point. The Banach Fixed Point Theorem says that every complete metric space has the BFPP. However, E.…
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…
The Brunn-Minkowski inequality, applicable to bounded measurable sets $A$ and $B$ in $\mathbb{R}^d$, states that $|A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}$. Equality is achieved if and only if $A$ and $B$ are convex and homothetic sets in…
In this paper we address the global stability problem for double-bubbles in the plane. This is accomplished by combining the "improved convergence theorem" for planar clusters developed in arXiv:1409.6652 with an ad hoc analysis of the…
For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…
We show that if $x$ is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good enough local approximation at $x$, then $x$ is already a denting point. It turns…
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…
We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the results obtained in the case of contractions defined on Banach spaces [Berinde, V.; P\u{a}curar, M.…
We establish two-point distortion theorems for sense-preserving planar harmonic mappings $f=h+\overline{g}$ which satisfies the univalence criteria in the unit disc such that, Becker's and Nehari`s harmonic version. In addition, we find the…
Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…
The notion of best approximation mapping (BAM) with respect to a closed affine subspace in finite-dimensional space was introduced by Behling, Bello Cruz and Santos to show the linear convergence of the block-wise circumcentered-reflection…
We study best approximations to compact operators between Banach spaces and Hilbert spaces, from the point of view of Birkhoff-James orthogonality and semi-inner-products. As an application of the present study, some distance formulae are…
We study the weakest convergence-type conditions for fixed point results for Banach and Kannan mappings. Building on Suzuki's weakest condition for Banach mappings and our previous result for Kannan mappings, we compare convergence…
In this article, we introduce a four-point analogue of Banach-type, Kannan-type, and Chatterjea-type contractions, and examine their properties. We establish sufficient conditions under which these mappings achieve fixed points in a…
Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\to…
Let $X$ be a metric space. Recently in~[1] it was considered a new type of mappings $T\colon X\to X$ which can be characterized as mappings contracting perimeters of triangles. These mappings are defined by the condition based on the…
Two retractions Q and R on closed convex cones M and respectively N of a Banach space are called mutually polar if Q+R=I and QR=RQ=0. This note investigates the existence of a pair of mutually polar retractions for given cones M and N. It…
For a nonempty convex subset $C$ of a Hadamard space $X$, it is proved that $u=P_Cx$ if and only if $\langle\overrightarrow{xu},\overrightarrow{uy}\rangle \geqslant0$ for all $y\in C$. As an application of this characterization, we prove…