Results 61 to 70 of about 741 (181)

A Fixed Point Free Nonexpansive Map [PDF]

Proceedings of the American Mathematical Society, 1981
In this note we give an example of a weakly compact convex subset of L 1 [ 0 , 1 ] {L_1}[0,1] that fails to have the fixed point property for nonexpansive maps. This answers a long-standing question which was recently raised again by S. Reich [7].
openaire   +2 more sources

On the Monotone Variational Inclusion Problems: A New Algorithm‐Based Modified Splitting Approach

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this paper, we introduce and analyze an inertial viscosity forward–backward splitting approach. We approximate a common solution of the monotone variational inclusion problem by using the demicontractive mapping in a real Hilbert space. It is shown that the sequence produced by our suggested algorithm has a strong convergence to a solution obtained ...
Uzoamaka A. Ezeafulukwe, George B. Akuchu, Sina Etemad, Austine E. Ofem, Godwin C. Ugwunnadi, Zaher Mundher Yaseen, Xian-Ming Gu   +6 more
wiley   +1 more source

Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces

Abstract and Applied Analysis, 2011
We introduce a new modified Halpern iteration for a countable infinite family of nonexpansive mappings {Tn} in convex metric spaces. We prove that the sequence {xn} generated by the proposed iteration is an approximating fixed point sequence of a ...
Withun Phuengrattana, Suthep Suantai
doaj   +1 more source

Best Proximity Points of Relatively Jaggi Nonexpansive Mappings in Busemann Convex Spaces

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this paper, we introduce cyclic (noncyclic) relatively Jaggi nonexpansive mappings on Busemann convex spaces and investigate the existence of their best proximity points (pairs). Furthermore, we extend the notation of relatively u‐continuous mappings in geodesic spaces and generalize an existence result of best proximity points from strictly convex ...
M. Gabeleh, M. Hassanvand, H. R. Salimi Moghaddam, Calogero Vetro   +3 more
wiley   +1 more source

On extremal nonexpansive mappings

Zeitschrift für Analysis und ihre Anwendungen
We study the extremality of nonexpansive mappings on a non-empty 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 Banach spaces with the Radon–Nikodym property and all
Christian Bargetz, Michael Dymond, Katriin Pirk   +2 more
openaire   +3 more sources

An Introduction to C∗‐Algebra‐Valued Metric‐Like Space With Related Applications

Journal of Mathematics, Volume 2025, Issue 1, 2025.
It is well‐known that the main objective of metric‐like spaces is to pave way for the development of fixed point results in nonstandard framework, such as in nonsymmetric distance structures, where self‐distances might be nonzero. This objective becomes more achievable when the range set of the distance function is a C∗‐algebra. Unfortunately, the idea
Zulaihatu Tijjani Ahmad, Mohammed Shehu Shagari, Maha Noorwali, Abba Ali Tijjani, Afis Saliu, Pramita Mishra   +5 more
wiley   +1 more source

On directionally nonexpansive mappings

European Journal of Mathematics
AbstractIn 2000, W.A. Kirk introduced the concept of directionally nonexpansive mappings. Here, we present a more comprehensive study of this class of mappings, including a fixed-point result for them. We further present a class of mappings, properly containing the directionally nonexpansive ones, for which Kirk’s theorem still holds.
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On Generalized (α‐ψ)‐Contraction With Rational Contraction Type on Generalized Metric Space Endowed With the Orthogonal Direct Sum

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This paper explores fixed point theory, focusing on (α‐ψ)‐contraction‐type operators defined on complete generalized metric spaces with an orthogonal direct sum structure. It establishes existence and uniqueness results under these extended contraction conditions.
Ghadah Albeladi, Saleh Omran, Ching-Feng Wen   +2 more
wiley   +1 more source

Strong convergence theorems for a sequence of nonexpansive mappings with gauge functions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013
In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gˆateaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞).
Cholamjiak Prasit, Je Cho Yeol, Suantai Suthep   +2 more
doaj   +1 more source

On Weak Compatible Mappings, 3‐D Column Graphs Approach in Multiplicative Generalized Metric Spaces With an Application

Journal of Mathematics, Volume 2025, Issue 1, 2025.
The purpose of this work is to investigate the approach to 3‐D column graphs in multiplicative generalized metric spaces (MGM‐spaces) utilizing single‐valued mappings with an application. In MGM‐space, we use weakly compatible four self‐mappings to prove common fixed point (CFP) results without requiring their continuity.
Saif Ur Rehman, Muhammad Sohail, Tayyab Mahmood, Hamza Ali Abujabal, Taoufik Moulahi, Muhammad Imran Haider, Ammar Alsinai   +6 more
wiley   +1 more source