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In this article, we introduce iterative methods (implicit and explicit) for finding a common fixed point set of a countable family of strict pseudo-contractions, which is a unique solution of some variational inequality. Furthermore, we prove the strong convergence theorems of such iterative scheme in a q-uniformly smooth Banach space which admits a weakly sequentially continuous generalized du...

In this paper, we introduce viscosity approximation methods based on generalized contractionmappings for finding a set of common fixed points of a countable family of strict pseudo-contractionmappings, the commonelement of the set solutions of a general system of variational inequalities with Lipschitzian and relaxed cocoercive mappings and the set of solutions of a generalizedmixed equilibrium...

We study a strategic game model on hypergraphs where players, modelled by nodes, try to coordinate or anti-coordinate their choices within certain groups of players, modelled by hyperedges. We show this model to be a strict generalisation of symmetric additively separable hedonic games to the hypergraph setting and that such games always have a pure Nash equilibrium, which can be computed in ps...

In this paper we construct a new variant of the Weil representation, associated with a symplectic vector space (V, ω) defined over a finite field of characteristic two. Our variant is a representation ρ : AMp (V ) → GL (H), where the group AMp (V ) is forth cover of a group ASp (V ), which is a nontrivial gluing of the symplectic group Sp (V ) and the dual group V ∗. In particular, the group AS...

We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, s...

Two results related to Mulholland inequality are presented. First, there are functions that are not geo-convex but solve Mulholland inequality; thus Mulholland’s condition is not necessary. Second, the set of functions that solve Mulholland inequality is not closed with respect to compositions. As a corollary, the dominance relation on the set of strict triangular norms is not transitive. The p...

We use a hybrid iterative method to find a common element of the set of fixed points of an infinite family of Lipschitzian quasi-nonexpansive mappings, the set of solutions of the general system of the variational inequality and the set of solutions of the generalized mixed equilibrium problem in real Hilbert spaces. We also show that our main strong convergence theorem for finding that common ...

Let {Si}i 1 be N strict pseudo-contractions defined on a closed and convex subset C of a real Hilbert space H. We consider the problem of finding a common element of fixed point set of these mappings and the solution set of a system of equilibrium problems by parallel and cyclic algorithms. In this paper, new iterative schemes are proposed for solving this problem. Furthermore, we prove that th...

Pseudo noun incorporation constructions in Sakha and Tamil obey a strict linear adjacency condition, such that not only the NP but its head noun must be adjacent to the verb at PF. I argue that this adjacency condition can be explained if the head of the NP adjoins to the verb to create a unit that is interpreted as a complex predicate at LF. The resulting structure can be linearized at PF if a...