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We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometries are extremal in this sense for many Banach spaces, including Banac
Externí odkaz:
http://arxiv.org/abs/2409.04292
Autor:
Lins, Brian
If a real analytic nonexpansive map on a polyhedral normed space has a nonempty fixed point set, then we show that there is an isometry from an affine subspace onto the fixed point set. As a corollary, we prove that for any real analytic 1-norm or $\
Externí odkaz:
http://arxiv.org/abs/2407.16671
Autor:
Bot, R. I., Zalinescu, C.
In this note, we demonstrate that an incorrect statement has been propagated in multiple papers, stemming from the substitution of ``lim'' with ``limsup'' for a sequence in Lemma 1.3 of the paper [J. Schu: Weak and strong convergence to fixed points
Externí odkaz:
http://arxiv.org/abs/2406.16378
Level proximal subdifferential was introduced by Rockafellar recently as a tool for studying proximal mappings of possibly nonconvex functions. In this paper we give a systematic study of level proximal subdifferntial, characterize variational convex
Externí odkaz:
http://arxiv.org/abs/2406.00648
Autor:
Popławski, Michał
A finite family $\mathcal{F}=\{f_1,\ldots,f_n\}$ of continuous selfmaps of a given metric space $X$ is called an iterated function system (shortly IFS). In a case of contractive selfmaps of a complete metric space is well-known that IFS has an unique
Externí odkaz:
http://arxiv.org/abs/2405.16977
Autor:
Alam, Aftab
In this paper, we introduce the notions of proximally completeness, proximally closedness and proximally continuity and utilize the same to prove a result on existence and uniqueness of best proximity points in the setting of metric space (not necess
Externí odkaz:
http://arxiv.org/abs/2405.02635
Autor:
Anjum, Rizwan, Abbas, Mujahid
In this note, we analyzed the concept of enriched nonexpansive which was proposed in "Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces" (Carpathian J. Math., 35(2019), No. 3, 293-304.) Through
Externí odkaz:
http://arxiv.org/abs/2405.07999
Autor:
Berinde, Vasile, Păcurar, Mădălina
The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings established b
Externí odkaz:
http://arxiv.org/abs/2404.04928
Autor:
Bauschke, Heinz H., Gao, Yuan
It is well known that the iterates of an averaged nonexpansive mapping may only converge weakly to fixed point. A celebrated result by Baillon, Bruck, and Reich from 1978 yields strong convergence in the presence of linearity. In this paper, we exten
Externí odkaz:
http://arxiv.org/abs/2404.04402
Autor:
Berinde, Vasile
We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in literature fr
Externí odkaz:
http://arxiv.org/abs/2404.04309