## Lecture Notes on Nonexpansive and Monotone Mappings in Banach SpacesCenter for Dynamical Systems, Division of Applied Mathematics, Brown University, 1967 - Banach spaces - 128 pages |

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### Contents

Preliminaries | 1 |

Nonexpansive mappings in Banach spaces | 22 |

Monotone mappings in Banach spaces | 62 |

1 other sections not shown

### Common terms and phrases

Acad adjoint mapping Amer assumption asymptotically regular ball boundary value problems bounded closed bounded sets bounded subset Bul1 closed and convex closed convex subset closed subset coercive mapping compact subset completes the proof convergent sequence convex Banach space convex closed convex set convex subset Corollary Definition demicompact densely defined dual space easily seen element equivalent Euclidean space exists finite dimensional subspaces finite intersection property fixed point follows immediately hemicontinuous hemicontinuous mapping Hence Hilbert space implies inequality 3.21 invariant isometric Lemma linear continuous functional linear mapping linear subspace mapping T:C maps bounded Math Minty monotone subset nonempty nonexpansive mapping nonlinear operators norm normal structure Proc Proposition 2.1 reflexive Banach space S(uq sequence of successive sequence xn set F solution of inequality successive approximations Theorem 3.1 theory of monotone Tx,x uniformly convex Banach Ux Ux vector weak topology weakly closed weakly compact weakly convergent