We show some sufficient conditions on a Banach space X concerning the generalized James constant, the generalized Jordan-von Neumann constant, the generalized Zbagănu constant, the coefficient ε̃0 X , the weakly convergent sequence coefficientWCS X , and the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings. These fixed point theor...

Geir Agnarsson, Jill Bigley Dunham.* George Mason University, Fairfax, VA. Extremal coin graphs in the Euclidean plane. A coin graph is a simple geometric intersection graph where the vertices are represented by non-overlapping closed disks in the Euclidean plane and where two vertices are connected if their corresponding disks touch. The problem of determining the maximum number of edges of a ...

Abstract We identify a norm-dense subspace of the dual sequence space $$l^{(p,\infty )}$$ l ( p , ∞ ) , thus closing existing gap in literature. based our approach on notion James...

We survey elementary results in Minkowski spaces (i.e. finite dimensional Banach spaces) that deserve to be collected together, and give simple proofs for some of them. We place special emphasis on planar results. Many of these results have often been rediscovered as lemmas to other results. In Part I we cover the following topics: The triangle inequality and consequences such as the monotonici...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

The concept of matroid, with its companion concept of geometric lattice, was distilled by Hassler Whitney [19], Saunders Mac Lane [10] and Garrett Birkhoff [2] from the common properties of linear and algebraic dependence. The inverse problem, how to represent a given abstract matroid as the matroid of linear dependence of a specified set of vectors over some field (or as the matroid of algebra...

This is the second part of a two-part paper on Birkhoff systems. A Birkhoff system is an algebra that has two binary operations · and +, with each being commutative, associative, and idempotent, and together satisfying x · (x + y) = x + (x · y). The first part of this paper described the lattice of subvarieties of Birkhoff systems. This second part continues the investigation of subvarieties of...

A Birkhoff system is an algebra that has two binary operations · and +, with each being commutative, associative, and idempotent, and together satisfying x · (x + y) = x + (x · y). Examples of Birkhoff systems include lattices, and quasilattices, with the latter being the regularization of the variety of lattices. A number of papers have explored the bottom part of the lattice of subvarieties o...