On a fixed point problem of Reich

In this paper, we give an affirmative answer to a fixed point problem of S.Reich.

     

A quantitative version of Kirk's fixed point theorem for asymptotic contractions

In [W.A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. 277 (2003) 645-650], W.A. Kirk introduced the notion of asymptotic contractions and proved a fixed point theorem for such mappings. Using techniques from proof mining, we develop a variant of the notion of asymptotic contractions and prove a quantitative version of the corresponding fixed point theorem.     

Global attractivity results for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem

In this paper, two results concerning the global attractivity and global asymptotic attractivity of the solutions for a nonlinear functional integral equation are proved via a variant of the Krasnoselskii fixed point theorem due to Dhage [B.C. Dhage, A fixed point theorem in Banach algebras with applications to functional integral equations, Kyungpook Math. J. 44 (2004) 145–155]. The investigations are placed in the Banach space of real functions defined, continuous and bounded on an unbounded interval. A couple of examples are indicated for demonstrating the natural realizations of the abstract results presented in the paper. Our results generalize the attractivity results of Banas and Rzepka [J. Banas, B. Rzepka, An application of measures of noncompactness in the study of asymptotic stability, Appl. Math. Lett. 16 (2003) 1–6] and Banas and Dhage [J. Banas, B.C. Dhage, Global asymptotic stability of solutions of a functional integral equations, Nonlinear Anal. (2007), doi:10.1016/j.na.2007.07.038], under weaker conditions with a different method.     

Common fixed point for generalized -weak contractions

In this paper we introduce the class of generalized (ψ,φ)-weak contractive mappings. We establish that these mappings necessarily have a unique common fixed point in complete metric spaces. This result generalizes an existing result in metric spaces.     

Four functionals fixed point theorem

The Four Functionals Fixed Point Theorem is a generalization of the original, as well as the functional generalizations, of the Leggett–Williams Fixed Point Theorem. In the Four Functionals Fixed Point Theorem, neither the upper nor the lower boundary of the underlying set is required to map below or above the boundary in the functional sense. As an application, the existence of a positive solution to a second-order right focal boundary value problem is considered by applying both standard and nonstandard choices of functionals. An extension to multivalued maps is provided for completeness.     

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.     

p-距离空间中的一类压缩映象的不动点定理

仿照距离空间,2-距离空间中的一些概念,引入了p-距离空间及p-距离空间中的一些基本概念.根据研究2-距离空间中不动点理论的思想和方法,利用泛函分析的理论,对p-距离空间中的不动点问题进行了研究.把2.距离空间中压缩型映像的不动点理论移植到了p-距离空间中,形成了p-距离空间中压缩型映像的一些基本不动点理论.其距.离空...     

Compression-expansion fixed point theorem in two norms and applications

In this paper we present a two-norms version of Krasnoselskii's fixed point theorem in cones. The abstract result is then applied to prove the existence of positive Lp solutions of Hammerstein integral equations with better integrability properties on the kernels.     

A definitive result on asymptotic contractions

We generalize a fixed point theorem for asymptotic contractions due to Kirk [W.A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. 277 (2003) 645-650]. Our result is the final generalization in some sense.     

Comment on: A new fixed point theorem in the fractal space

In this paper, we give a counterexample to Lemma 2.2 proved by Song-il Ri (2016). Further, we improve the result of Song-il Ri by employing a proper setting.     

A generalization of the Lefschetz fixed point theorem and detection of chaos

We consider the problem of existence of fixed points of a continuous map in (possibly) noninvariant subsets. A pair of subsets of induces a map given by if and elsewhere. The following generalization of the Lefschetz fixed point theorem is proved: If is metrizable, and are compact ANRs, and is continuous, then has a fixed point in provided the Lefschetz number of is nonzero. Actually, we prove an extension of that theorem to the case of a composition of maps. We apply it to a result on the existence of an invariant set of a homeomorphism such that the dynamics restricted to that set is chaotic.

     

Ekeland变分原理的推广及Caristi不动点定理在半度量空间的推广形式

本证明了半度量空间中的Ekeland变分原理及Caristic不动点定理．进而证明了半度量空间中的压缩映像原理。     

A surjection theorem and a fixed point theorem for a class of positive operators

This paper is concerned with α-convex operators on ordered Banach spaces. A surjection theorem for 1-convex operators in order intervals is established by means of the properties of cone and monotone iterative technique. It is assumed that 1-convex operator A is increasing and satisfies Ay−Ax?M(y−x) for θ?x?y?v₀, where θ denotes the zero element and v₀ is a constant. Moreover, we prove a fixed point theorem for -convex operators by using fixed point theorem of cone expansion. In the end, we apply the fixed point theorem to certain integral equations.     

The Schauder fixed point theorem in geodesic spaces

We give a direct proof of Schauder's fixed point theorem in the setting of geodesic metric spaces, generalizing the classical Schauder's theorem and improving a recent version of this theorem in CAT(κ)$\mathrm{CAT}(\kappa )$ spaces. As an application we prove an existence result for a variational inequality in the setting of CAT(κ)$\mathrm{CAT}(\kappa )$ spaces.     

A fixed point theorem for o‐minimal structures

We prove a definable analogue to Brouwer's Fixed Point Theorem for o‐minimal structures of real closed field expansions: A continuous definable function mapping from the unit simplex into itself admits a fixed point, even though the underlying space is not necessarily topologically complete. Our proof is direct and elementary; it uses a triangulation technique for o‐minimal functions, with an application of Sperner's Lemma. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Schauder-type fixed point theorem

In this brief note we study Schauder's second fixed point theorem in the space $(\mathit{BC},6\cdot 6)$ of bounded continuous functions $\varphi :[0,\infty )\to {\Re }^n$ with a view to reducing the requirement that there is a compact map to the requirement that the map is locally equicontinuous. Several examples are given, both motivating and applying the theory.     

A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point

If is a complete metric space and is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader mappings.