Europe's green thumb firmly on nose

On Firmly Nonexpansive Mappings

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...

Bacterial flagella are firmly anchored.

There are mutants of Salmonella enterica (with mutations in fliF and fliL) that shed flagella when they are swimming in a viscous medium or on the surface of soft agar. Filaments with hooks and the distal rod segment FlgG are recovered. We tried to extract flagellar filaments from such cells by pulling on them with an optical trap but failed, even when we used forces large enough to straighten ...

On the Nose

Firmly Focussed: Australia’s Future Productivity Growth

Firmly pseudo-contractive mappings and fixed points

We give some fixed point theorems for firmly pseudo-contractive mappings defined on nonconvex subsets of a Banach space. We also prove some fixed point results for firmly pseudo-contractive mappings with unbounded nonconvex domain in a reflexive Banach space.