Smoothness and rotundity in quotient spaces

Control and Cybernetics Rotundity, Smoothness and Duality

The duality between smoothness and rotundity of functions is studied in a nonlinear abstract framework. Here smoothness is enlarged to subdifferentiability properties and rotundity is formulated by means of approximation properties.

A Bornological Approach to Rotundity and Smoothness Applied to Approximation

In this paper we are interested in examining the geometry of a bounded convex function over a Banach space via its subdiierential mapping. We will consider two concepts. The rst is the single valuedness and continuity of the subdiierential mapping, and the second is the single valuedness and the continuity of the \inverse" of this mapping. The smoothness of f is important for the rst concept as...

Best Coapproximation in Quotient Spaces

As a counterpart to best approximation, a new kind of approximation, called best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi. In this paper, we use this coapproximation to prove some results on the existence and uniqueness of best coapproximation in quotient spaces when the underlying spaces are metric linear spaces. We shall also see how coproximinality ...

ε-weakly Chebyshev subspaces and quotient spaces

Extreme Points and Rotundity of Orlicz-sobolev Spaces