Right quadruple convexity

Mathematics, 2022

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Journal of Mathematical Analysis and Applications, 2012

We study some properties of O-convex and P-convex spaces and give a new proof of the P(n)-convexity of ℓ p sums of P(n)-convex spaces. Further we show using Ramsey's theorem that the space E β is P-convex. We define some moduli that characterize O-convexity and P-convexity and compare them to a modulus defined by García Falset. This enables us to establish some fixed point theorems. By means of several examples, we separate P-convexity from several geometrical conditions known to imply the fixed point property (FPP).

Texts in Applied Mathematics, 2001

Carpathian Journal of Mathematics, 2017

A set S in Rd is called it-convex if, for any two distinct points in S, there exists a third point in S, such that one of the three points is equidistant from the others. In this paper we first investigate nondiscrete it-convex sets, then discuss about the it-convexity of the eleven Archimedean tilings, and treat subsequently finite subsets of the square lattice. Finally, we obtain a lower bound on the number of isosceles triples contained in an n-point it-convex set.

2000

In this paper we introduce a quotient class of pairs of convex bodies in which every member have convex union.

UPI Journal of Mathematics and Biostatistics , 2018

The main purpose of this research is to develop a little further the m-convexity on real linear spaces introduced by Toader in 1984 from the settheoretic point of view. We prove that the family of m-convex sets has the algebraic structure of a complete partial ordered cone and is a proper subfamily of the well known family of starshaped sets respect to the origin. Moreover, we define the corresponding m-convex hull and present a formula to compute it depending on the regular and well known convex hull. Finally, a result of the Carath´eodory-type for m-convex sets is shown.

Numerical Functional Analysis and Optimization

Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal convolution, normal cone, conjugate function, subdifferential, are studied thoroughly in this paper. Among other things, we show how a generalized polyhedral convex set can be characterized via the finiteness of the number of its faces. In addition, it is proved that the infimal convolution of a generalized polyhedral convex function and a polyhedral convex function is a polyhedral convex function. The obtained results can be applied to scalar optimization problems described by generalized polyhedral convex sets and generalized polyhedral convex functions.

Pacific Journal of Mathematics, 1981

Studia Mathematica, 2011

We prove that a closed convex subset C of a complete linear metric space X is polyhedral in its closed linear hull if and only if no infinite subset A ⊂ X\C can be hidden behind C in the sense [x, y] ∩ C = ∅ for any distinct points x, y ∈ A.