Adrian Petrusel

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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)
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)
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)
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, an existence theorem for n th 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(More)
We establish some strong sufficient conditions that the inequality f 4 (x, y, z) ≥ 0 holds for all nonnegative real numbers x, y, z, where f 4 (x, y, z) is a cyclic homogeneous polynomial of degree four. In addition, in the case f 4 (1, 1, 1) = 0 and also in the case when the inequality f 4 (x, y, z) ≥ 0 does not hold for all real numbers x, y, z, we(More)