Results 101 to 110 of about 21,184 (145)

Maximal Monotone Mappings

, 1990
The logical structure of this chapter is represented in Figures 32.1 and 32.2. The key to our approach is the main theorem on pseudomonotone perturbations of maximal monotone mappings due to Browder (1968) (Theorem 32. A in Section 32.4). This theorem will be proved via the Galerkin method.
E. Zeidler
semanticscholar   +2 more sources

Differential Inclusions with Maximal Monotone Maps

, 1984
We devote this chapter to a very important class of differential inclusions $$x'\left( t \right) \in - A\left( {x\left( t \right)} \right)$$ (1) where A(x) ≐ −F(x)is a so-called “maximal monotone” set-valued map.
J. Aubin, A. Cellina
semanticscholar   +2 more sources

A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings

SIAM Journal on Control and Optimization, 2000
Summary: We consider the forward-backward splitting method for finding a zero of the sum of two maximal monotone mappings. This method is known to converge when the inverse of the forward mapping is strongly monotone. We propose a modification to this method, in the spirit of the extragradient method for monotone variational inequalities, under which ...
Paul Tseng
exaly   +3 more sources

Non-convex perturbations of maximal monotone differential inclusions

Israel Journal of Mathematics, 1983
A. Cellina, M. Marchi
exaly   +2 more sources

A Strong Convergence Theorem for an Iterative Method for Finding Zeros of Maximal Monotone Maps with Applications to Convex Minimization and Variational Inequality Problems

Proceedings of the Edinburgh Mathematical Society, 2018
Let E be a uniformly convex and uniformly smooth real Banach space, and let E* be its dual. Let A : E → 2E* be a bounded maximal monotone map. Assume that A−1(0) ≠ Ø. A new iterative sequence is constructed which converges strongly to an element of A−1(0)
C. E. Chidume, M. Uba, M. I. Uzochukwu, E. Otubo, K. O. Idu   +4 more
semanticscholar   +1 more source

Geometric approach to the Moore–Penrose inverse and the polar decomposition of perturbations by operator ideals

Forum mathematicum, 2023
We study the Moore–Penrose inverse of perturbations by a proper symmetrically-normed ideal of a closed range operator on a Hilbert space. We show that the notion of essential codimension of projections gives a characterization of subsets of such ...
E. Chiumiento, Pedro Massey
semanticscholar   +1 more source

On the homotopy property of topological degree for maximal monotone mappings

Applied Mathematics and Computation, 2009
The purpose of the present paper is to study a homotopy property of the degree for maximal monotone mappings, and fill the lack of this important property in one of the papers of the first author [Appl.\ Math.\ Mech., Engl.\ Ed.\ 11, No.\,5, 441--454 (1990; Zbl 0895.47044)].
Yuqing Chen, Donal O'Regan
openaire   +2 more sources

The surjectivity of semiregular maximal monotone random mappings

rose, 2002
Let \(\Omega\) be a complete measurable space with a \(\sigma\)-algebra \(\Sigma\) and let \(X\) be a Banach space with its dual \(X^*\). Let \(D\) be a subset of \(X\). A mapping \(A: D\to X^*\) is called 1) monotone if \(\langle Ax-Ay,x-y \rangle\geq 0,\forall x,y\in D\); 2) maximal monotone if \(A\) is monotone and from \((x_0,x_0^*)\in X\times X^*,\
Chuong, Nguyen Minh, Thuan, Nguyen Xuan
openaire   +2 more sources

New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators

Applied Mathematics and Computation, 2011
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Yongfu Su, Mengqin Li, Hong Zhang
openaire   +2 more sources