ON THE CLASS OF RELATIVELY WEAKLY DEMICOMPACT NONLINEAR OPERATORS.

In this paper we discuss some topological properties of the set F(S0, T,z):= {x ∊ X : S0 x ∊ Tx + zg, where T is a nonlinear multi-valued mappings and S0 is a single-valued mappings acting on a Banach space X. This study is based on a new concept, the so called weakly relative demicompactness for nonlinear operators. [ABSTRACT FROM AUTHOR]