ON THE MAXIMALITY OF SUMS OF TWO MAXIMAL MONOTONE OPERATORS
DOI:
https://doi.org/10.5281/mnzpd194Abstract
Abstract. Let E be a real reflexive Banach space, E∗ be the dual space of
E and T : D(T) ⊆ E → 2
E∗
, S : D(S) ⊆ E → 2
E∗
be two maximal monotone
operators. Assume that L : E → (−∞, +∞) is a bounded function, i.e., maps
a bounded subset of E to a bounded subset of R, and γ : E → R is a function.
Suppose that
(g, x − y) ≥ L(x) + γ(y)
for all x ∈ D(T), g ∈ T x and y ∈ E. Then S + T is also a maximal monotone
operator.
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