We prove a variant of the well-known Reidemeister-Schreier Theorem for finitely L-presented groups. More precisely, we prove that each finite index subgroup of a finitely L-presented group is itself finitely L-presented. Our proof is constructive and it yields a finite L-presentation for the subgroup. We further study conditions on a finite index subgroup of an invariantly finitely L-presented ...

There are many notions of discrete convexity of polyominoes (namely hvconvex [1], Q-convex [2], L-convex polyominoes [5]) and each one has been deeply studied. One natural notion of convexity on the discrete plane leads to the definition of the class of hv-convex polyominoes, that is polyominoes with consecutive cells in rows and columns. In [1] and [6], it has been shown how to reconstruct in ...

In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

In this paper, a von Neumann-type inequality is studied on an Eaton triple $ (V,G,D) $, where V real inner product space, G compact subgroup of the orthogonal group O (V) and D \subset closed convex cone. By using structure triple, refinement shown. special case = ( ) Cauchy-Schwarz obtained.

Let C be a nonempty closed convex subset of a real Banach space E. Let S : C → C be a quasi-nonexpansive mapping, let T : C → C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F := {x ∈ C : Sx = x and Tx = x} 6 = ∅. Let {xn}n≥0 be the sequence generated from an arbitrary x0 ∈ C by xn+1 = (1− cn)Sxn + cnT xn, n ≥ 0. We prove necessary and sufficient conditions fo...

We construct a homogeneous connected Polish space X on which no א0-bounded topological group acts transitively. In fact, X is homeomorphic to a convex subset of Hilbert space `.

Let K be a bounded, closed and convex subset of a Banach space X. We show that the iterates of a typical element (in the sense of Baire category) of a class of nonexpansive mappings which take K to X converge uniformly on K to the unique fixed point of this typical element.

In this paper, we prove the following results: Let K be a closed convex subset of a real Banach space E. Let T := {T (t) | t ∈ R+} be strongly continuous semigroup of asymptotically nonexpansive mappings from K into K such that F (T ) := ∩t∈R+F (T (t)) 6= ∅, where F (T (t)) = {x ∈ K |T (t)x = x} and R+ denotes the set of nonnegative real numbers. Then for arbitrary x0 ∈ K, the implicit iteratio...

The authors exhibit an abelian group not embeddable in a product of copies of Z (the integers) but totally orderable so that every covering pair of convex subgroups has archimedean quotient isomorphic to Z (= g.d.), thus furnishing a counterexample to Théorème 4 on p. 53 of [21]; then go on to show that every countable g.d. group is algebraically free (§4); and purport to show it also embeddabl...