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We introduce two notions of a contractive orbit of a set-valued map defined in a first countable space. The first defines the contraction with respect to the topology of the underlying space while the second defines the contraction with…

Functional Analysis · Mathematics 2026-02-10 Detelina Kamburova

The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its…

Algebraic Topology · Mathematics 2024-05-31 Jose Manuel Garcia Calcines

Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous…

Optimization and Control · Mathematics 2025-09-05 Yair Censor , Daniel Reem , Maroun Zaknoon

We study a generalization of the Svarc genus of a fiber map. For an arbitrary collection E of spaces and a map f:X-->Y, we define a numerical invariant, the E-sectional category of f, in terms of open covers of Y. We obtain several basic…

Algebraic Topology · Mathematics 2007-05-23 Martin Arkowitz , Jeffrey Strom

This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, we provide a complete and self-contained proof that…

Functional Analysis · Mathematics 2025-09-15 Faruk Alpay , Hamdi Alakkad

The main result of this paper is a fixed point result relating the spreading model structure of Banach spaces and Schauder basis with not too large basis constant. As a striking consequence, we deduce that every super-reflexive space has…

Functional Analysis · Mathematics 2023-03-22 Cleon S. Barroso

We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…

Functional Analysis · Mathematics 2026-03-24 Vladyslav Babenko , Vira Babenko , Oleg Kovalenko

In this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a Banach space. We also study a Schauder fixed point property for a semitopological semigroup of…

Functional Analysis · Mathematics 2012-07-20 A. T. -M. Lau , Yong Zhang

The aim of this study to investigate the existence of solutions for the following nonlocal integral boundary value problem of Caputo type fractional differential inclusions. To achieve our goals, we take advantage of fixed point theorems…

Classical Analysis and ODEs · Mathematics 2018-07-17 Hüseyin Işık

For a bounded closed convex set $K$, in this note, we study the FPP for $\alpha$-H\"older nonexpansive maps, i.e. mappings $T\colon K\to K$ for which $\|T x -Ty\| \leq\| x - y\|^\alpha$ for all $x, y\in K$, $\alpha\in (0,1)$. First, we note…

Functional Analysis · Mathematics 2022-12-20 Cleon S. Barroso

In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.

General Topology · Mathematics 2018-09-12 Yaé Ulrich Gaba

We study the approximate fixed point property (AFPP) for continuous single-valued functions and for continuous multivalued functions in digital topology. We extend what is known about these notions and discuss errors that have appeared in…

General Topology · Mathematics 2020-01-20 Laurence Boxer

An w-limit set of a continuous self-mapping of a compact metric space X is said to be totally periodic if all of its points are periodic. We say that X has the w-FTP property provided that for each continuous self-mapping f of X, every…

Dynamical Systems · Mathematics 2019-03-26 Habib Marzougui , Issam Naghmouchi

We study the fixed point theory of n-valued maps of a space X using the fixed point theory of maps between X and its configuration spaces. We give some general results to decide whether an n-valued map can be deformed to a fixed point free…

Geometric Topology · Mathematics 2017-02-17 Daciberg Lima Gonçalves , John Guaschi

Let Y be a locally convex Hausdorff space, K \subset E a cone and \leq_K the partial order defined by K. Let (X, p) be a TV S- cone metric space, {\phi} : K \rightarrow K a vectorial comparison function and f : X \rightarrow X such that…

Functional Analysis · Mathematics 2011-11-15 Ion Olaru

The paper discusses the conditions for the existence of fixed points of multivalued mappings that are not based on the linear structure of the set. The descriptions for the sets of fixed points for mappings with closed graph in compact…

General Topology · Mathematics 2016-02-23 Dmitrii Serkov

Given a path-connected space $X$ and $H\leq\pi_1(X,x_0)$, there is essentially only one construction of a map $p_H:(\widetilde{X}_H,\widetilde{x}_0)\rightarrow(X,x_0)$ with connected and locally path-connected domain that can possibly have…

Algebraic Topology · Mathematics 2020-01-01 Hanspeter Fischer , Jacob D. Garcia

A topological group $G$ has the Approximate Fixed Point (AFP) property on a bounded convex subset $C$ of a locally convex space if every continuous affine action of $G$ on $C$ admits a net $(x_i)$, $x_i\in C$, such that…

Group Theory · Mathematics 2021-02-18 Cleon S. Barroso , Brice R. Mbombo , Vladimir G. Pestov

The genus of a fibration was introduced by Schwarz in 1962. Given a continuous map $g:A\to B$, the usual sectional number $\text{sec}_u(g)$ is the least integer~$m$ such that $B$ can be covered by $m$ open subsets, each of which admits a…

Algebraic Topology · Mathematics 2024-10-31 Cesar A. Ipanaque Zapata

In this paper, first we have established two sets of sufficient conditions for a TS-IF contractive mapping to have unique fixed point in a intuitionistic fuzzy metric space. Then we have defined \,$(\,\epsilon \,,\, \lambda\,)$\,…

General Mathematics · Mathematics 2011-03-16 T. K. Samanta , Sumit Mohinta