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It is shown that a separable Banach space $X$ can be given an equivalent norm $|\!|\!|\cdot |\!|\!|$ with the following properties:\quad If $(x_n)\subseteq X$ is relatively weakly compact and $\lim_{m\to\infty} \lim_{n\to\infty}\break…
In this paper, we study a new iterative method for finding the fixed point of a weak Bregman relatively nonexpansive mapping and the set of solutions of generalized mixed equilibrium problems in Banach spaces.
We prove that a Banach space has the uniform approximation property with proportional growth of the uniformity function iff it is a weak Hilbert space.
We prove that every continuous mapping from a separable infinite-dimensional Hilbert space $X$ into $\mathbb{R}^{m}$ can be uniformly approximated by $C^\infty$ smooth mappings {\em with no critical points}. This kind of result can be…
In this work, using a new geometrical approach we study to the existence of the fixed-point of mappings that independence of the smoothness, and also of their single-values or multi-values. This work proved the theorems that generalize in…
In this paper the weak topology on a normed space is studied from the viewpoint of infinite-dimensional topology. Besides the weak topology on a normed space $X$ (coinciding with the topology of uniform convergence on finite subsets of the…
We consider $L$-$\omega$-nonexpansive maps $T\colon K\to K$ on a convex subset $K$ of a Banach space $X$, i.e., maps in which $\omega_T(\delta)\leq L\delta +\omega(\delta)$ with $L\in [0,1]$, $\omega$ being a modulus of continuity and…
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…
We study the existence of fixed points for continuous maps $f$ from an $n$-ball $X$ in $\mathbb R^n$ to $\mathbb R^n$ with $n\geq 1$. We show that $f$ has a fixed point if, for some absolute retract $Y\subset\partial X$, $f(Y)\subset X$ and…
Suppose that $Q$ is a weak$^{\ast }$ compact convex subset of a dual Banach space with the Radon-Nikod\'{y}m property. We show that if $(S,Q)$ is a nonexpansive and norm-distal dynamical system, then there is a fixed point of $S$ in $Q$ and…
We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed…
In this paper we generalize to unbounded convex subsets C of hyperbolic spaces results obtained by W.A. Kirk and R. Espinola on approximate fixed points of nonexpansive mappings in product spaces $(C\times M)_\infty$, where M is a metric…
Kohlenbach and Leustean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty $UCW$-hyperbolic space has a fixed point. In this paper, we adapt a construction due to Moloney in order to provide a…
In this paper we show that every sequence (F_n) of finite dimensional subspaces of a real or complex Banach space with increasing dimensions can be ``refined'' to yield an F.D.D. (G_n), still having increasing dimensions, so that either…
This article generalizes the work of Ballmann and \'Swiatkowski to the case of Reflexive Banach spaces and uniformly convex Busemann spaces, thus giving a new fixed point criterion for groups acting on simplicial complexes.
In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\{T_j\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of…
In this paper we survey known results of characterizations of reflexive Banach spaces, which are based on convergence of usual and generalized arithmetic mean (or Ces\`aro sum), weakly compact subsets, affine sets in a Banach space or its…
We investigate typical properties of nonexpansive mappings on unbounded complete hyperbolic metric spaces. For two families of metrics of uniform convergence on bounded sets, we show that the typical nonexpansive mapping is a Rakotch…
A Banach space $X$ has the $2$-summing property if the norm of every linear operator from $X$ to a Hilbert space is equal to the $2$-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent…
We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the results obtained in the case of contractions defined on Banach spaces [Berinde, V.; P\u{a}curar, M.…