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...

There seems to be a love-hate relationship between Brouwer's fixed point theorem and the fundamental theorem of algebra; in this note we offer one more tweak at it, and give a version of Rouchés theorem.

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.

Using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of Monge-Amp`{e}re equations are established‎.‎

in this paper, vector ultrametric spaces are introduced and a fixed point theorem is given forcorrespondences. our main result generalizes a known theorem in ordinary ultrametric spaces.

The influence of fixed point theorems for contractive and nonexpansive mappings see 1, 2 on fixed point theory is so huge that there are many results dealing with fixed points of mappings satisfying various types of contractive and nonexpansive conditions. On the other hand, it is also huge that well-known Brouwer’s and Schauder’s fixed point theorems for set-contractive mappings exert an influ...

So Brouwer’s Fixed Point Theorem asserts that each Dn, n ≥ 1, is a fixed point domain. On the other hand, Dn less a point, [0, 1]∪ [2, 3] and R are not fixed point domains. (It is easy to construct appropriate functions with no fixed point for these sets.) The fact that Dn is compact is important in Brouwer’s Fixed Point Theorem. However, if G is a fixed point domain, and f : G → H is a continu...

In this paper is introduced a new type of generalization of metric spaces called $S_b$ metric space. For this new kind of spaces it has been proved a common fixed point theorem for four mappings which satisfy generalized contractive condition. We also present example to confirm our theorem.

In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.