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

100%
Petruşel A., Yao J.-C.
Open Mathematics
|
2009
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tom 7
|
nr 2
335-347
EN
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.
2
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An abstract Cauchy problem for higher order functional differential inclusions with infinite delay

81%
Ke T., Obukhovskii V., Wong N.-C., Yao J.-C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2011
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tom 31
|
nr 2
199-229
EN
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.
3
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On asymptotics of solutions for a class of functional differential inclusions

81%
Kornev S., Obukhovskii V., Yao J.-C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2014
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tom 34
|
nr 2
219-227
EN
We define a non-smooth guiding function for a functional differential inclusion and apply it to the study the asymptotic behavior of its solutions.
4
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On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

81%
Kamenskii M., Obukhovskii V., Yao J.-C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2013
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tom 33
|
nr 2
193-204
EN
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.
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