We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.

We study maps of positive operators of the Schatten -classes (), which preserve the -norms of convex combinations, that is, . They are exactly those carrying the form for a unitary or antiunitary . In the case , we have the same conclusion whenever it just holds for all the positive Hilbert-Schmidt class operators of norm . Some examples are demonstrated.

This paper is devoted to the study of orthogonality and disjointness preserving linear maps between Fourier and FourierStieltjes algebras of locally compact groups. We show that a linear bijection : A (G 1) A (G 2)(resp. : B (G 1) B (G 2)) between two Fourier algebras (resp. FourierStieltjes algebras) of locally compact groups will induce a topological group isomorphism between G 1 and G 2, provided that preserves both disjointness and some kind of orthogonality. This improves earlier results of JJ Font and MS Monfared, where amenability of the groups or continuity of the linear maps are assumed. We also study the structure of bounded and unbounded disjointness preserving linear functionals of Fourier algebras. In the development, general results about disjointness and orthogonality preserving linear maps between C-algebras, W-algebras and their preduals are obtained.

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The object of this paper is to establish an existence result for nonlinear inequalities for not necessarily pseudomonotone maps. As a consequence of our result, we give some existence results for variational and variational-like inequalities.