Sentence examples for modulus of convexity from inspiring English sources

We define the modulus of convexity for a convex subset of a Banach space; see also [3].

Let be a uniformly convex Banach space with modulus of convexity and let be a nonempty bounded closed convex subset of.

A Banach space is said to be uniformly convex if the modulus of convexity of is as follows: (2.1).

A real Banach space is said to be uniformly convex if the modulus of convexity of : (2.1).

A Banach space is said to be a uniformly convex if the modulus of convexity of is (2.1).

Let be a uniformly convex hyperbolic space with modulus of convexity, and let.

A uniformly convex space X has modulus of convexity of power type p if, for some (0< K

First, we do not impose that the metric is convex and, second, our modulus of convexity does depend on the two variables r and ε while it is assumed to depend only on ε in [11].

Let be a real uniformly convex Banach space with the modulus of convexity of power type.

If a uniformly convex metric space admits a modulus of convexity such that it is lower semicontinuous from the right with respect to (for each fixed ) then we say is a lower semicontinuous from the right modulus of convexity for.

If a uniformly convex metric space admits a modulus of convexity such that it decreases with (for each fixed ) then we say that is a monotone modulus of convexity for.