The research topics investigated by our group range from Real to Functional Analysis. The main themes in Real Analysis are continuity and related questions; lower semicontinuity, quasi-continuity and its generalizations. The main themes in Functional Analysis deal with the Geometry of Banach Spaces, especially
- Estimations of the retraction constant. It is known that there exists an universal constant K such that for every infinite dimensional Banach space X there exists a Lipschitzian retraction of the unit ball B(X) onto its boundary S(X) with a Lipschitzian constant less than K. This result suggests some quantitative problems. First of all it seems that no significant lower and no upper bound for the best constant K is known. However some estimations of K(X) for some classical Banach spaces, such as Hilbert spaces or L1 ([0,1]), are available in literature. We will look for sharp estimations.
- Medians and Chebyshev centers: problems about existence, unicity, stability
- Theory of fixed points of contractive mappings