In this paper we introduce the concepts of upper and lower weakly B*continuous multifunction, and obtain some characterizations and several properties concerning upper and lower B*-continuous as well as upper and lower weakly B*continuous multifunction. The relationship between these multifunctions and their graphs are investigated.

In this note we prove that the weak topology of a Banach space has the Continuous Representability Property which means that every (weakly) continuous total preorder defined on a Banach space can be represented by a weakly continuous utility function. This shows that weak topologies are perfect to look for continuous utility functions that represent preferences on infinite-dimensional commodity...

We first include a result of the second author showing that the Banach space S is complementably minimal. We then show that every block sequence of the unit vector basis of S has a subsequence which spans a space isomorphic to its square. By the Pe lczyński decomposition method it follows that every basic sequence in S which spans a space complemented in S has a subsequence which spans a space ...

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using a tehnique based on a continuous selection, we establish new existence results for the equilibrium of the abstract economies. The constraint correspondences ...