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...

This paper presents an iterative method for solving the generalized nonlinear set-valued mixed quasi-variational inequality, a problem class that was introduced by Huang, Bai, and Kang, [Comp. Math. Appl., 40, 2000]. The method incorporates step size controls that enable application to problems where certain set-valued mappings do not always map to nonempty closed bounded sets.

The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point...

We give stationary point theorems of set-valued mappings in complete and compact metric spaces. The results in this note generalize a few results due to Fisher. 2000 Mathematics Subject Classification. 54H25.

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , where X is a Σ-product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

We denote by σ(F,E) the topology on F generated by the family {ω(x, ε) : x ∈ E, ε > 0} as a subbase for the neighbourhood system at 0. It is easy to show that, if F possesses the σ(F,E)-topology, F becomes a locally convex topological vector space. The σ(E,F )-topology on E is defined analogously. A subset X of E is said to be σ(E,F )-compact if X is compact related to the σ(E,F )-topology. Let...

*Correspondence: [email protected] 1Dpto. de Análisis Matemático, IMUS (Instituto Matemático de la Universidad de Sevilla), Universidad de Sevilla, C/Tarfia s/n, 41012 Sevilla, Spain Full list of author information is available at the end of the article Abstract In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of...

This paper concerns the study of the so-called super minimizers related to the concept of super efficiency in constrained problems of multiobjective optimization, where cost mappings are generally set-valued. We derive necessary conditions for super minimizers on the base of advanced tools of variational analysis and generalized differentiation that are new in both finite-dimensional and infini...

In this paper, we introduce an iterative method for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusions with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of an equilibrium problem in Hilbert spaces. Furthermore, using our new iterative scheme, unde...