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Multivalued fractals in b-metric spaces

Monica BoriceanuMarius BotaAdrian Petruşel — 2010

Open Mathematics

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...

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

Bupurao C. DhageAdrian Petruşel — 2006

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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].

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.

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