A Kleinian group Γ is a discrete subgroup of PSL2(C). When non-elementary, such a group possesses a unique non-empty minimal closed invariant subset ΛΓ of the Riemann sphere, called the limit set. A Kleinian group acts properly discontinuously on the complement ∆Γ of ΛΓ and so this set is called the domain of discontinuity. Such a group is said to be convex co-compact if it acts co-compactly on...

We make a connection between the structure of bidisc and distinguished subgroup its automorphism group. The group bidisc, as we know, is dimension six acts transitively. observe that it contains isomorphic to open unit disc this partitions into complex curve family strongly pseudo-convex hypersurfaces are non-spherical CR-manifolds. Our work reverses process shows any 2-dimensional Kobayashi-hy...

Let X be either a uniformly convex Banach space or a reflexive Banach space having the Opial property. It is shown that a multivalued nonexpansive mapping on a bounded closed convex subset of X has an endpoint if and only if it has the approximate endpoint property. This is the first result regarding the existence of endpoints for such kind of mappings even in Hilbert spaces. The related result...

In this paper, we prove the analog to Browder and Göhde fixed point theorem for G-nonexpansive mappings in complete hyperbolic metric spaces uniformly convex. In the linear case, this result is refined. Indeed, we prove that if X is a Banach space uniformly convex in every direction endowed with a graph G, then every G-nonexpansive mapping T : A → A, where A is a nonempty weakly compact convex ...

We study the proximal point algorithm with Bregman type distance to minimize the problem , , . ) ( min S x to s x f ∈ where S is an open convex subset of a complete simply connected Riemannian manifold M of non positive sectional curvature and f is a convex function in this manifold. Introducing a strong assumption on the geodesic triangle on this manifold we obtain the convergence of the seque...

In this paper, weak and strong convergence of two-step iteration sequences to a common fixed point for a pair of a finite family of asymptotically nonexpansive mappings and a finite family of generalized nonexpansive multivalued mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented. The results obtained in this paper extend and improve some recent known res...

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

Given a combinatorial description C of a polyhedron having E edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize C is generally not a convex subset of R [9]. If C has five or more faces, Andreev’s Theorem states that the corresponding space of dihedral angles AC obtained by restricting to non-obtuse angles is a convex polytope. In this paper we explain why Andre...

Let C be a nonempty closed convex subset of a uniformly convex Banach space E with a Fr6chet differentiable norm, G a right reversible semitopological semigroup, and S {S(t) :t E G} a continuous representation of G as mappings of asymptotically nonexpansive type of C into itself The weak convergence of an almost-orbit {u(t) :t E G} of S {S(t) :t 6 G} on C is established. Furthermore, it is show...

For given k ∈ (0, 1) and r > 0, a self-mapping T : M → M is said to be r-roughly k-contractive provided ‖Tx− Ty‖ ≤ k ‖x− y‖+ r (x, y ∈ M). To state fixed-point properties of such a mapping, the self-Jung constant Js(X) is used, which is defined as the supremum of the ratio 2 rconv S(S)/ diam S over all non-empty, non-singleton and bounded subsets S of some normed linear space X, where rconv S(S...