We consider a generalized equation governed by strongly monotone and Lipschitz single-valued mapping maximally set-valued in Hilbert space. are interested the sensitivity of solutions w.r.t. perturbations both mappings. demonstrate that directional differentiability solution map can be verified using operator resolvent mapping. The result is applied to quasi-generalized equations which we have ...

Throughout this paper, let Z, E, and F be topological vector spaces, let X ⊆ E and Y ⊆ F be nonempty, closed, and convex subsets. Let D : X → 2X , T : X → 2Y and Ψ : X ×Y × X → 2Z be set-valued mappings, and let C : X → 2Z be a set-valued mapping such that C(x) is a closed pointed and convex cone with intC(x) = ∅ for each x ∈ X , where intC(x) denotes the interior of the set C(x). Then the gene...

A general nonlinear regularity model for a set-valued mapping F : X × R+ ⇒ Y , where X and Y are metric spaces, is studied using special iteration procedures, going back to Banach, Schauder, Lyusternik and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal. Appl., 118 (1986) and employ it to obtain basic estimates for exploring regularity/openness properties. We also show...

We study stability properties of a proximal point algorithm for solving the inclusion 0 ∈ T (x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact pr...

We are interested in existence results for nonconvex functional differential inclusions. First, we prove an existence result, in separable Hilbert spaces, for first order nonconvex sweeping processes with perturbation and with delay. Then, by using this result and a fixed point theorem we prove an existence result for second order nonconvex sweeping processes with perturbation and with delay of...

Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f:X → Y is a Frechet differentiable function and F:X ⇉ 2 is a set-valued mapping with closed graph. Uniform convergence of Chord method for solving generalized equation y ∈ f x + F x ...... . (∗), where y ∈ Y a parameter, is studied in the present paper. More clearly, we obtain the uniform convergence of the se...

We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms, accepted for publication, DOI 10.1007/s11075-011-9490-5]. The SCNPP with only two s...