Zeros and Mapping Theorems for Perturbations of m-Accretive Operators in Banach Spaces

摘要

Let X be a real Banach space and T : D(T) is contained in X →2~X be an m-accretive operator. Let C : D(T) is contained in X→ X be a bounded operator (not necessarily continuous) such that C(T +I)~(-1) is compact. Suppose that for every x ∈ D(T) with ||x|| > r, there exists jx ∈ Jx such that < u + Cx,jx > ≥ 0, (*) for all u ∈ Tx. Then, we have 0 ∈ (T + C)(D(T) ∩ B_r(0)), where B_r(0) denotes the open ball of X with centre at zero and radius r > 0. Assume, furthermore, that T : D(T) → 2~X is strongly accretive. Then, 0 ∈ (T + C)(D(T) ∩ B_r(0)). As applications of the above zero theorem, we derive many new mapping theorems for perturbations of m-accretive operators in Banach spaces. When, T and C are odd operators, we also obtain some new mapping theorems.