Monotonicity in Functional Analysis
In functional analysis on a topological vector space X, a (possibly non-linear) operator T : X → X∗ is said to be a monotone operator if
Kachurovskii's theorem shows that convex functions on Banach spaces have monotonic operators as their derivatives.
A subset G of X × X∗ is said to be a monotone set if for every pair and in G,
G is said to be maximal monotone if it is maximal among all monotone sets in the sense of set inclusion. The graph of a monotone operator G(T) is a monotone set. A monotone operator is said to be maximal monotone if its graph is a maximal monotone set.
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