Related papers: Browder's Theorem: from One-Dimensional Parameter …
We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)
In this paper using Sperner's lemma for modified partition of a simplex we will constructively prove Brouwer's fixed point theorem for sequentially locally non-constant and uniformly sequentially continuous functions.
As an application of Brouwer's fixed-point theorem we prove that a continuously differentiable convex function with gradient of constant norm is an affine mapping. It is a first-order characterization of affine mappings among continuously…
If $f:[a,b]\to \mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\mathbb{C}\to\mathbb{C}$ is map and $X$ is a continuum. We extend…
Brouwer's fixed point theorem from 1911 is a basic result in topology - with a wealth of combinatorial and geometric consequences. In these lecture notes we present some of them, related to the game of HEX and to the piercing of multiple…
Brouwer's fixed point theorem states that any continuous function from a closed $n$-dimensional ball to itself has a fixed point. In 1961, Klee showed that if such a function has discontinuities that are bounded, then it has a point that is…
We extend the fixed point result for Path-Averaged Contractions (PA-contractions) from complete metric spaces to complete b-metric spaces. We prove that every PA-contraction on a complete b-metric space has a unique fixed point, provided…
More than a century ago, L. E. J. Brouwer proved a famous theorem, which says that any orientation preserving homeomorphism of the plane having a periodic point must have a fixed point. In recent years, there are still some authors giving…
It is investigated in what sense the Brouwer fixed point theorem may be viewed as a corollary of the Lawvere fixed point theorem. A suitable generalisation of the Lawvere fixed point theorem is found and a means is identified by which the…
We establish the first common fixed point theorem for commutative set-valued mappings. This may help to generalize common fixed point theorems in single-valued setting to those in set-valued. We also prove the existence of a fixed point in…
We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…
A well-known result from Brouwer states that any orientation preserving homeomorphism of the plane with no fixed points has an empty non-wandering set. In particular, an invariant compact set implies the existence of a fixed point. In this…
A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…
For a Hausdorff space $X$, we exhibit an unexpected connection between the sectional number of the Fadell-Neuwirth fibration $\pi_{2,1}^X:F(X,2)\to X$, and the fixed point property (FPP) for self-maps on $X$. Explicitly, we demonstrate that…
In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality of integral type depended on another function. This conditions is analogous of Banach…
A self-map $T$ of a $\nu$-generalized metric space $(X,d\,)$ is said to be a Ciric-Matkowski contraction if $d(Tx,Ty)<d(x,y)$, for $x\neq y$, and, for every $\epsilon>0$, there is $\delta>0$ such that $d(x,y)<\delta+\epsilon$ implies…
The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial…
We show the direct applicability of the Brouwer fixed point theorem for the existence of equilibrium points and periodic solutions for differential systems on general domains satisfying geometric conditions at the boundary. We develop a…
In this paper, we investigate the existence and uniqueness of fixed points for self-mappings defined on bipolar metric spaces using a new class of contractive conditions, namely polynomial-type contractions. Our main results establish…
Let $D$ be a bounded domain in a complex Banach space. According to the Earle-Hamilton fixed point theorem, if a holomorphic mapping $F : D \mapsto D$ maps $D$ strictly into itself, then it has a unique fixed point and its iterates converge…