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The surjectivity of semiregular maximal monotone random mappings
rose, 2002Let \(\Omega\) 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
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Differential Inclusions with Maximal Monotone Maps
1984We 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.
Jean-Pierre Aubin, Arrigo Cellina
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Applied Mathematics and Computation, 2011
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Yongfu Su, Mengqin Li, Hong Zhang
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Yongfu Su, Mengqin Li, Hong Zhang
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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.
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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.
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Shrinking Projection Methods for Maximal Monotone Operators and Quasi-nonexpansive Mappings
2010 International Conference on Computational Aspects of Social Networks, 2010In this paper, we consider a new shrinking projection method for finding common elements of the set of fixed points of a quasi-φ-nonexpansive mapping and the set of zero points of a maximal monotone operator. We establish a strong convergence theorem of common elements by using new analysis techniques in the setting of reflexive, strictly convex ...
Xinghui Gao, Lerong Ma
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Journal of Optimization Theory and Applications, 2012
The author suggests some extensions of the known Browder and Halpern strong convergence results for iterative approximation processes in Hilbert spaces. These results are adjusted for finding common solutions of variational inequalities and zero points of several monotone type mappings. Some relations with other recent results are also discussed.
W Takahashi
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The author suggests some extensions of the known Browder and Halpern strong convergence results for iterative approximation processes in Hilbert spaces. These results are adjusted for finding common solutions of variational inequalities and zero points of several monotone type mappings. Some relations with other recent results are also discussed.
W Takahashi
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Stability of the maximal measure for piecewise monotonic interval maps
Ergodic Theory and Dynamical Systems, 1997Let $T:X\to{\Bbb R}$ be a piecewise monotonic map, where $X$ is a finite union of closed intervals. Define $R(T)=\bigcap_{n=0}^{\infty} \overline{T^{-n}X}$, and suppose that $(R(T),T)$ has a unique maximal measure $\mu$. The influence of small perturbations of $T$ on the maximal measure is investigated.
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A new class of general variational inclusions involving maximal $\eta$-monotone mappings
Publicationes Mathematicae Debrecen, 2003Summary: A new class of maximal \(\eta\)-monotone mappings is introduced and studied in Hilbert spaces and the Lipschitz continuity of the resolvent operator for maximal \(\eta\)-monotone mappings is proved in this paper. We also introduce and study a new class of general variational inclusions involving maximal \(\eta\)-monotone mappings and construct
Huang, Nan-Jing, Fang, Ya-Ping
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Nonlinear Analysis: Theory, Methods & Applications, 2004
This article deals with some generalization of the Browder degree theory for mappings of the type \(T + A: \;X \to X^*\), where \(T\) is a bounded demicontinuous \((S)_{(+)}\)-mapping and \(A\) a maximal monotone operator (\(X\) denoting a reflexive Banach space).
Kobayashi, Jun, Ôtani, Mitsuharu
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This article deals with some generalization of the Browder degree theory for mappings of the type \(T + A: \;X \to X^*\), where \(T\) is a bounded demicontinuous \((S)_{(+)}\)-mapping and \(A\) a maximal monotone operator (\(X\) denoting a reflexive Banach space).
Kobayashi, Jun, Ôtani, Mitsuharu
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Products of Finitely Many Resolvents of Maximal Monotone Mappings in Reflexive Banach Spaces
SIAM Journal on Optimization, 2011We propose two algorithms for finding (common) zeros of finitely many maximal monotone mappings in reflexive Banach spaces. These algorithms are based on the Bregman distance related to a well-chosen convex function and improve previous results.
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