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An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

Adrian PetruşelJen-Chih Yao — 2009

Open Mathematics

In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.

On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

Mikhail KamenskiiValeri ObukhovskiiJen-Chih Yao — 2013

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.

An abstract Cauchy problem for higher order functional differential inclusions with infinite delay

Tran Dinh KeValeri ObukhovskiiNgai-Ching WongJen-Chih Yao — 2011

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.

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