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A new convexity property that implies a fixed point property for L 1

Chris Lennard (1991)

Studia Mathematica

In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result...

A new series of conjectures and open questions in optimization and matrix analysis

Jean-Baptiste Hiriart-Urruty (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review 49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.

A new series of conjectures and open questions in optimization and matrix analysis

Jean-Baptiste Hiriart-Urruty (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.

A new type of orthogonality for normed planes

Horst Martini, Margarita Spirova (2010)

Czechoslovak Mathematical Journal

In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions d ≥ 3 .

A note on equality of functional envelopes

Martin Kružík (2003)

Mathematica Bohemica

We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in ℝ m × n , min ( m , n ) ≤ 2 , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.

A note on formal power series

Xiao-Xiong Gan, Dariusz Bugajewski (2010)

Commentationes Mathematicae Universitatis Carolinae

In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series g is convex and balanced which implies that the subset 𝕏 ¯ g consisting of formal power series which can be composed by a formal power series g possesses such properties. We also provide a necessary and sufficient condition for the superposition operator T g to map 𝕏 ¯ g into itself or to map 𝕏 g into...

Currently displaying 101 – 120 of 2516