Monotonicity of the complementary vector field of a nonexpansive map
SZ Németh - Acta Mathematica Hungarica, 1999 - Springer
Acta Mathematica Hungarica, 1999•Springer
Abstract The Minty-Browder monotonicity notion will be generalized for vector fields of a
Riemannian manifold M. If M is a Hadamard manifold, complementary vector fields of maps
f: M→ M will be introduced. If f is nonexpansive it is proved that the complementary vector
field of f is monotone. In particular, compositions of projection maps onto convex sets will be
considered.
Riemannian manifold M. If M is a Hadamard manifold, complementary vector fields of maps
f: M→ M will be introduced. If f is nonexpansive it is proved that the complementary vector
field of f is monotone. In particular, compositions of projection maps onto convex sets will be
considered.
Abstract
The Minty-Browder monotonicity notion will be generalized for vector fields of a Riemannian manifold M. If M is a Hadamard manifold, complementary vector fields of maps f : M → M will be introduced. If f is nonexpansive it is proved that the complementary vector field of f is monotone. In particular, compositions of projection maps onto convex sets will be considered.
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