It is shown that the inverse limit of an inverse system of smooth continua is a smooth continuum provided that there exists a thread composed of initial points and that the bonding mappings are monotone relative to these points. It also is proved that the property of being an arboroid, a dendroid, a generalized tree, a fan or a smooth fan is an invariant under the inverse limit operation if the...

In this paper, we provide a regularization method for finding a solution of Noor’s variational inequality problem induced by a hemicontinuous monotone operator. Moreover, such a solution is related to the set of zero of inverse strongly monotone mappings. Consequently, since we do not assume the strong monotonicity of the considered operator, our results are general and extend some well-known r...

This paper aims at studying the convergence of some iteration processes for mixed variational inequalities with convex nondifferentiable functionals and J -potential, J -coercive, J -pseudomonotone or J -strongly inverse monotone operators in uniformly smooth Banach spaces. Our results generalize corresponding theorems of [I.B. Badriev, O.A. Zadvornov, A decomposition method for variational ine...

We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in ...

and Applied Analysis 3 Let C be a nonempty closed convex subset of a real Hilbert space H. Recall that a mapping A : C → H is called α-inverse strongly monotone if there exists a positive real number α such that 〈Ax − Ay, x − y〉 ≥ α‖Ax −Ay‖, for all x, y ∈ C. It is clear that any αinverse strongly monotone mapping is monotone and 1/α-Lipschitz continuous. Let f : C → H be a ρ-contraction; that ...

Let [Formula: see text], [Formula: see text], and [Formula: see text] be a strongly monotone and Lipschitz mapping. A Krasnoselskii-type sequence is constructed and proved to converge strongly to the unique solution of [Formula: see text]. Furthermore, our technique of proo f is of independent interest.

in this paper we propose a descent method for solving variational inequality problems where the underlying operator is nonsmooth, locally Lipschitz, and monotone over a closed, convex feasible set. The idea is to combine a descent method for variational inequality problems whose operators are nonsmooth, locally Lipschitz, and strongly monotone, with the Tikonov-Browder regularization technique....