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.

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, we give a new fixed point theorem forweakly quasi-contraction maps in metric spaces. our results extend and improve some fixed point and theorems in literature.

Proving  fixed point theorem in a fuzzy metric space is not possible for  Meir-Keeler contractive mapping. For this, we introduce the notion of $c_0$-triangular fuzzy metric space. This new space allows us to prove some fixed point theorems for  Meir-Keeler contractive mapping. As some pattern we introduce the class of $alphaDelta$-Meir-Keeler contractive and we establish some results of fixed ...

1 The Borsuk-Ulam theorem We have seen how combinatorics borrows from probability theory. Another area which has been very beneficial to combinatorics, perhaps even more surprisingly, is topology. We have already seen Brouwer's fixed point theorem and its combinatorial proof. Theorem 1 (Brouwer). For any continuous function f : B n → B n , there is a point x ∈ B n such that f (x) = x. A more po...