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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
|
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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The method of upper and lower solutions for perturbed nth order differential inclusions

100%
Dhage B., Petruşel A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2006
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tom 26
|
nr 1
57-76
EN
In this paper, an existence theorem for nth order perturbed differential inclusion is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions on the multi-functions involved in the inclusion. Our results extend the existence results of Dhage et al. [7,8] and Agarwal et al. [1].
3
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Multivalued fractals in b-metric spaces

81%
Boriceanu M., Bota M., Petruşel A.
Open Mathematics
|
2010
|
tom 8
|
nr 2
367-377
EN
Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal operators. On the other hand, the most common setting for the study of fractals and multi-fractals is the case of operators on complete or compact metric spaces. The purpose of this paper is to extend the study of fractal operator theory for multivalued operators on complete b-metric spaces.
4
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Fixed point theorems for set-valued Y-contractions

81%
Rus I., Petruşel A., Petruşel G.
Banach Center Publications
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2007
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tom 77
|
nr 1
227-237
EN
The purpose of this paper is to present several fixed point theorems for the so-called set-valued Y-contractions. Set-valued Y-contractions in ordered metric spaces, set-valued graphic contractions, set-valued contractions outside a bounded set and set-valued operators on a metric space with cyclic representations are considered.
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