Adrian Petruşel

Fixed point theorems in ordered L-spaces

The purpose of this paper is to present some fixed point results in ordered L-spaces. Our results generalize and extend a recent result of Ran and Reurings (2004). Some applications to matrix equations are also considered.

Multivalued fractals in b-metric spaces

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.

Data dependence of the fixed point set of some multivalued weakly Picard operators

In this paper we study data dependence of the fixed point set for a special class of multivalued weakly Picard operators. Existence and data dependence of the common fixed points for some Reich-type multivalued operators are also proved. Finally, an application to a Fredholm integral inclusion is given.

Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph

Abstract The purpose of this paper is to present some fixed point results for self-generalized (singlevalued and multivalued) contractions in ordered metric spaces and in metric spaces endowed with a graph. Our theorems generalize and extend some recent results in the literature.

Ulam-Hyers Stability for Operatorial Equations

Ulam-Hyers Stability for Operatorial Equations Using the weakly Picard operator technique, we present some Ulam-Hyers stability results for coincidence point problems for multivalued operators.

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

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.

FIXED POINTS AND HOMOTOPY RESULTS FOR ĆIRIĆ-TYPE MULTIVALUED OPERATORS ON A SET WITH TWO METRICS

The purpose of this paper is to present some fixed point results for nonself multivalued operators on a set with two metrics. In addition, a homotopy result for multivalued operators on a set with two metrics is given. The data dependence and the well-posedness of the fixed point problem are also discussed.

Vector-valued metrics, fixed points and coupled fixed points for nonlinear operators

In this paper, we will present fixed point theorems for singlevalued and multivalued operators in spaces endowed with vector-valued metrics, as well as a Gnana Bhaskar-Lakshmikantham-type theorem for the coupled fixed point problem, associated to a pair of singlevalued operators (satisfying a generalized mixed monotone property) in ordered metric spaces. The approach is based on Perov-type fixed point theorems in spaces endowed with vector-valued metrics. The Ulam-Hyers stability and the limit shadowing property of the fixed point problems are also discussed.MSC:47H10, 54H25.

Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems

We suggest and analyze relaxed extragradient iterative algorithms with regularization for finding a common element of the solution set of a general system of variational inequalities, the solution set of a split feasibility problem, and the fixed point set of a strictly pseudocontractive mapping defined on a real Hilbert space. Here the relaxed extragradient methods with regularization are based on the well-known successive approximation method, extragradient method, viscosity approximation method, regularization method, and so on. Strong convergence of the proposed algorithms under some mild conditions is established. Our results represent the supplementation, improvement, extension, and development of the corresponding results in the very recent literature.

A fixed point theorem for cyclic generalized contractions in metric spaces

In this paper, we extend a recent result of V. Pata (J. Fixed Point Theory Appl. 10:299-305, 2011) in the frame of a cyclic representation of a complete metric space.