We consider the forward-backward splitting method for nding 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 modiication to this method, in the spirit of the extragradient method for monotone variational inequalities, under which the method converges assuming only the forward mapping i...

In this paper, we investigate the global well-posedness and existence of strong exponential attractors for a nonlinear strongly damped hyperbolic equation in \begin{document}$ \Omega\subset{\mathbb R}^N $\end{document}: style='text-indent:20px;'> \begin{document}...

An artin algebra A is said to be a higher Auslander provided the global dimension and dominant coincide. We say that linear Nakayama monotone, its Kupisch series first increases, then decreases. are going classify monotone algebras which algebras. Let us stress classification strongly depends on parity of A.

In this paper, we prove the existence theorem for a mapping defined by T = T1 + T2 when T1 is a μ1-Lipschitz continuous and γ-strongly monotone mapping, T2 is a μ2-Lipschitz continuous mapping, we have a mapping T is Lipschitz continuous but not strongly monotone mapping. This work is extend and improve the result of N. Petrot [17]. Mathematics Subject Classification: 46C05, 47D03, 47H09, 47H10...

We investigate the convergence rates of the trajectories generated by implicit first and second order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space. We show that these trajectories strongly converge with exponential rate to a zero of the sum, provided the latter is st...

We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. ...

MOTIVATION Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties. RESULTS The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsyst...