A fixed point theorem including the last theorem of Poincaré

Poincaré's last theorem is the most famous among those theorems which are not subsumed by the Lefschetz fixed point theorem. A fixed point theorem is proved directly and constructively which in a special case reduces to the last theorem of Poincaré.     

A GENERALIZATION OF CLARKE＇S FIXED POINT THEOREM

This paper proposes a formally stronger set-valued Claxke‘s fixed point theorem. By this-theorem we can improve a fixed point theorem for weakly inward contraction set-valued mapping of D. Dowing and W.A. Kirk.     

A fixed point theorem for weakly Zamfirescu mappings

In [5], Zamfirescu (1972) gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan, and Chatterjea. In this paper, we follow the ideas of Dugundji and Granas to extend Zamfirescu’s fixed point theorem to the class of weakly Zamfirescu maps. A continuation method for this class of maps is also given.     

A NOVEL FIXED POINT THEOREM AND ITS APPLICATIONS

In this article, a novel fixed point theorem in C[0,1] space is established by using the properties of fixed point index. This theorem is then applied to prove the existence of positive solutions for three-point boundary value problems and generalizes some previous results.     

A fixed point theorem for the infinite-dimensional simplex

We define the infinite-dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^∞, and prove that this space has the fixed point property: any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find an approximate fixed point; the proof relies on elementary analysis and Sperner's lemma. The fixed point theorem is shown to imply Schauder's fixed point theorem on infinite-dimensional compact convex subsets of normed spaces.     

A fixed point theorem involving a hybrid inwardness-contraction condition

A fixed point theorem is proved which involves a hybrid inwardness-contraction condition and simultaneously extends three earlier results of NADLER, CLARKE and REICH, respectively. The aim of this paper is to prove a fixed point theorem which will simultaneously extends three earlier results of NADLER [5], CLARKE [2], and REICH [7], respectively.     

A new type of fixed point theorem in metric spaces

We prove a generalization of Edelstein’s fixed point theorem. Though there are thousands of fixed point theorems in metric spaces, our theorem is a new type of theorem.     

A common fixed point theorem with applications to vector equilibrium problems

In this paper, using the Brouwer fixed point theorem, we establish a common fixed point theorem for a family of set-valued mappings. As applications of this result we obtain existence theorems for the solutions of two types of vector equilibrium problems, a Ky Fan-type minimax inequality and a generalization of a known result due to Iohvidov.     

Generalized Browder-type fixed point theorem with strongly geodesic convexity on Hadamard manifolds with applications

In this paper, a generalized Browder-type fixed point theorem on Hadamard manifolds is introduced, which can be regarded as a generalization of the Browder-type fixed point theorem for the set-valued mapping on an Euclidean space to a Hadamard manifold. As applications, a maximal element theorem, a section theorem, a Ky Fan-type Minimax Inequality and an existence theorem of Nash equilibrium for non-cooperative games on Hadamard manifolds are established.     

A fixed point theorem of Jungck in $$b_v(s)$$-metric spaces

In this paper, we prove the common fixed point theorem of Jungck in \(b_v(s)\)-metric spaces. As a corollary, a common fixed point theorem in the rectangular b-metric space and the well known common fixed point theorem in b-metric spaces are obtained.     

Remarks on Caristi’s fixed point theorem and Kirk’s problem

Without assumptions on the continuity and the subadditivity of η, by means of Caristi’s fixed point theorem, we investigated the existence of fixed points for a Caristi type mapping which partially answered Kirk’s problem and improved Caristi’s fixed point theorem, Jachymski’s fixed point theorem and Khamsi’s fixed point theorem since φ is not necessarily assumed to be bounded below on X.     

The Hyers theorem via the Markov–Kakutani fixed point theorem

We present an application of the Markov–Kakutani common fixed point theorem to the theory of stability of functional equation by proving some version of the Hyers theorem concerning approximate homomorphisms.     

The Kakutani fixed point theorem for Roberts spaces

Roberts spaces were the first examples of compact convex subsets of Hausdorff topological vector spaces (HTVS) where the Krein–Milman theorem fails. Because of this exotic quality they were candidates for a counterexample to Schauder's conjecture: any compact convex subset of a HTVS has the fixed point property. However, extending the notion of admissible subsets in HTVS of Klee [Math. Ann. 141 (1960) 286–296], Ngu [Topology Appl. 68 (1996) 1–12] showed the fixed point property for a class of spaces, including the Roberts spaces, he called weakly admissible spaces. We prove the Kakutani fixed point theorem for this class and apply it to show the non-linear alternative for weakly admissible spaces.     

A fixed point theorem for multifunctions and an application

The main result is a fixed point theorem for compositions of chain faithful multifunctions (Corollary 2.3). The theorem is then applied to get sufficient conditions for the fixed point property of the product of two partially ordered sets.Presented by R. P. Dilworth.     

Common fixed point theorem for hybrid generalized multi-valued contraction mappings

In this paper, we introduce the notion of a hybrid generalized multi-valued contraction mapping and establish the common fixed point theorem for this mapping. Our results generalize, unify, extend and complement several common fixed point theorems of many authors in the literature.     

A fixed point theorem

We establish a fixed point theorem for a Lie group of isometries acting on a Riemannian manifold with nonnegative curvature.     

On a fixed point theorem of Kirk

W.A. Kirk [J. Math. Anal. Appl. 277 (2003) 645-650] first introduced the notion of asymptotic contractions and proved the fixed point theorem for this class of mappings. In this note we present a new short and simple proof of Kirk's theorem.     

Edelstein's fixed point theorem in topological spaces

An extension to topological spaces of a wellknown fixed point theorem of M. Edelstein for contractive mappings on metric spaces is presented. Results based on the generalized Edelstein's theorem are also established concerning the existence of fixed points of continuous selfmaps on a topological space. As a special case a compact starshaped subset of a linear topological space is considered. The results extend the fixed point theoremsfor nonexpansive mappings on a compact metric space of L.F.Guseman, Jr. and B.C. Peters, Jr.     

A fixed point theorem for a family of mappings in a fuzzy metric space

In this paper we give a common fixed point theorem for a family of mappings of a G-complete fuzzy metric space (X, M, *) into itself. From this result we deduce a common fixed point theorem for a family of mappings of a complete metric space (X, d) into itself. Supported by University of Palermo.     

Further generalizations of the Gale-Nikaido-Debreu theorem

A fixed point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subsets of a t.v.s. is applied to generalize Gwinner’s extensions of the Walras excess demand theorem and of the Gale-Nikaido-Debreu theorem.