We construct one-step iterative process for an α- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study △-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.

Radial lines, suitably parameterized, are geodesics, but notice that the distance from the origin to the (Euclidean) unit sphere is infinite. This model makes it intuitively clear that the boundary at infinity of hyperbolic space is Sn−1. Hyperbolic space together with its boundary at infinity has the topology of a closed ball, and isometries of hyperbolic space extend uniquely to a homeomorphi...

We establish a relationship among the normal surface theory, Thurston’s algebraic gluing equation for hyperbolic metrics and volume optimization of generalized angle structures on triangulated 3-manifolds. The main result shows that a critical point of the volume on generalized angle structures either produces a solution to Thurston’s gluing equation or a branched normal surfaces with at most t...

In the space of cubic polynomials, Milnor defined a notable curve S p , consisting polynomials with periodic critical point, whose period is exactly . this paper, we show that for any integer ≥ 1 bounded hyperbolic component on Jordan disk.

A cubic polynomial with a marked fixed point 0 is called an IS-capture if it has Siegel disk D around and contains eventual image of critical point. We show that any on the boundary unique bounded hyperbolic component parameter space determined by rational lamination map relate polynomials to principal domain its closure.

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process hyperbolic plane. show that critical probability for existence of an infinite cluster tends to 1/2 as intensity infinity. This confirms conjecture Benjamini and Schramm [5].

Here we say that a real polynomial is hyperbolic or Axiom A, if the real line is the union of a repelling hyperbolic set, the basin of hyperbolic attracting periodic points and the basin of infinity. We call a C1 endomorphism of the compact interval (or the circle) hyperbolic if it has finitely many hyperbolic attracting periodic points and the complement of the basin of attraction of these poi...