Related papers: On a converse to Banach's Fixed Point Theorem
A Banach space $X$ has the ball fixed point property (BFPP) if for every closed ball $B$ and for every nonexpansive mapping $T\colon B\to B$, there is a fixed point. We study the BFPP for $C(K)$-spaces. Our goal is to determine topological…
A Banach space has the weak fixed point property if its dual space has a weak$^*$ sequentially compact unit ball and the dual space satisfies the weak$^*$ uniform Kadec-Klee property; and it has the \fpp if there exists $\epsilon>0$ such…
We show that the direct sum of Banach spaces $X_{1},..., X_{r}$ with a strictly monotone norm has the weak fixed point property for nonexpansive mappings whenever $M(X_{i})>1$ for each $i=1,...,r$. In particular, $(X_{1} \oplus ... \oplus…
A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…
Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach space has the fixed point property. After surveying classical…
The famous Banach Contraction Principle holds in complete metric spaces, but completeness is not a necessary condition -- there are incomplete metric spaces on which every contraction has a fixed point. The aim of this paper is to present…
The Banach contraction principle is the most celebrated fixed point theorem, it has been generalized in various directions. In this paper, inspired by the concept of $(\phi, F)-$contraction in metric spaces, introduced by Wardowski. We…
We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a mapping also respects matrix similarities, i.e., is a…
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…
We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the…
In this paper we show that if $(y_n)$ is a seminormalized sequence in a Banach space which does not have any weakly convergent subsequence, then it contains a wide-$(s)$ subsequence $(x_n)$ which admits an equivalent convex basic sequence.…
In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to…
In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are…
By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction…
Assume that $X$ is a Banach space of measurable functions for which Koml\'os' Theorem holds. We associate to any closed convex bounded subset $C$ of $X$ a coefficient $t(C)$ which attains its minimum value when $C$ is closed for the…
In this article we extend the notion of orthogonal metric space to weak orthogonal metric space. Then we establish fixed point results for a mapping satisfying a more general contraction condition. Several nontrivial examples are given in…
This paper deals with the \emph{Bishop-Phelps-Bollob\'as property} (\emph{BPBp} for short) on bounded closed convex subsets of a Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove that the \emph{BPBp} holds for…
This paper brings new results on the FPP in Banach spaces $X$ with a Schauder basis. We first deal with the problem of whether there is a Banach space isomorphic to $\co$ having the FPP. We show that the answer is negative if $X$ contains a…
In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use…
A space X has the local fixed point property LFPP, (local periodic point property LPPP) if it has an open basis $\mathcal{B}$ such that, for each $B\in \mathcal{B}$, the closure $\overline{B}$ has the fixed (periodic) point property. Weaker…