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...

Approximation-solvability of a class of nonlinear implicit variational inequalities involving a class of partially relaxed monotone mappings a computation-oriented class in a Hilbert space settingis presented with some applications. Partially Strongly Monotone Mapping, Partially Relaxed Mono

In this paper, we introduce a new iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inversestrongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common el...

We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. ...

In this paper we introduce a viscosity relaxed-extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space H . The viscosity relaxed-extragradient method is based on two methods: extragradientlike approximation method and ...

Mapping composition is a fundamental operation in metadata driven applications. Given a mapping over schemas σ1, σ2, and σ3, the composition problem is to find an equivalent mapping over only σ1 and σ3. We describe a new composition algorithm that targets practical applications. It incorporates view unfolding. It eliminates as many σ2 symbols as possible, even if not all can be eliminated. It c...

Such a set G is said to be maximal monotone if it is maximal among monotone sets in the sense of set inclusion, and a mapping T is said to be maximal monotone if its graph G(T) is a maximal monotone set. For reflexive Banach spaces X and mappings T with D(T)~X, the basic result obtained independently by Browder [2] and Minty [20] states that if T is a monotone operator from D(T)=X to X* which i...

Let H be a real Hilbert space. A mapping A : D(A) ⊆ H → H is said to be monotone if ⟨Ax − Ay, x − y⟩ ≥ 0 for every x, y ∈ D(A). A is called maximal monotone if it is monotone and the R(I + rA) = H, the range of (I + rA), for each r > 0, where I is the identity mapping on H. A is said to satisfy the range condition if cl(D(A)) ⊆ R(I + rA) for each r > 0. For monotone mappings, there are many rel...

In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fix...

We introduce and study a new class of nonlinear general A-monotone operator equations with multivalued operator. By using Alber’s inequalities, Nalder’s results, and the new proximal mapping technique, we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general A-monotone operator equations and study the approximationsolvability of the nonlinear oper...