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The purpose of this paper is to present data dependence results for some multivalued weakly Picard operatorors such as: Reich-type operators, graphic-contractions.

- Lu-Chuan Ceng, Adrian Petrusel, Jen-Chih Yao
- Applied Mathematics and Computation
- 2009

In this paper we extend the notion of I 0 −continuity and uniform I 0 − continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators. 0 −continuity, semi-continuous set-valued operators, Hausdorff-Pompeiu generalized… (More)

The purpose of this paper is to present several characterizations for the concept of weakly Picard operator in K-metric spaces. Some new characterizations and applications, as well as, several open questions are also discussed.

In this paper we will present an abstract point of view on iterative approximation schemes of fixed points for multivalued operators. More precisely, we suppose that the algorithms are convergent and we will study the impact of this hypothesis in the theory of operatorial inclusiosns: data dependence, stability and Gronwall type lemmas. Some open problems… (More)

- Oana Mleşniţe, Adrian Petruşel
- 2013

Let X, Y be two nonempty sets and s, t : X → Y be two single-valued operators. By definition, a solution of the coincidence problem for s and t is a pair (x * , y *) ∈ X × Y such that s(x *) = t(x *) = y *. It is well-known that a coincidence problem is, under appropriate conditions, equivalent to a fixed point problem for a single-valued operator generated… (More)

In this paper, we consider the split feasibility problem (SFP) in infinite-dimensional Hilbert spaces, and study the relaxed implicit extragradient-like methods for finding a common element of the solution set Γ of the SFP and the set Fix(S) of fixed points of a nonexpansive mapping S. Combining Mann's implicit iterative method and Korpelevich's… (More)

- Cristina Urs, Adrian Petruşel
- 2013

In this paper, we present existence, uniqueness and Ulam-Hyers stability results for the coupled fixed points of a pair of contractive type singlevalued and respectively multivalued operators on complete metric spaces. The approach is based on Perov type fixed point theorem for contractions in spaces endowed with vector-valued metrics.

In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping.… (More)

We consider a semilinear differential inclusion and we obtain sufficient conditions for h-local controllability along a reference trajectory.