Results 51 to 60 of about 5,440 (186)

On the fixed points of affine nonexpansive mappings

International Journal of Mathematics and Mathematical Sciences, 2001
Let K be a closed convex bounded subset of a Banach space X and let T:K→K be a continuous affine mapping. In this note, we show that (a) if T is nonexpansive then it has a fixed point, (b) if T has only one fixed point then the mapping A=(I+T)/2 is a ...
Hülya Duru
doaj   +1 more source

Nonexpansive Mappings in Locally Convex Spaces [PDF]

Canadian Mathematical Bulletin, 1977
Recently Bruck initiated the study of the structure of the fixed-point set of a nonexpansive selfmap T of a Banach space, where T satisfies a conditional fixed point property. We generalize many of his results to a Hausdorff locally convex space X. Also, we generalize a result of Holmes and Narayanaswami and use it, along with a procedure of Kiang, to ...
Hicks, Troy L., Kubicek, John D.
openaire   +2 more sources

Stationary and Nonstationary Iterative Methods for Generalized Nonexpansive Mappings in Uniformly Convex Banach Spaces

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
The aim of this paper is to present a novel stationary and nonstationary iterative approach for approximating common fixed points of a finite family of generalized nonexpansive mappings in uniformly convex Banach spaces. For the stationary scheme, both strong and weak convergence theorems are established under standard geometric conditions.
Sehar Afsheen, Amna Kalsoom, Faryad Ali, Akbar Azam, John R. Akeroyd   +4 more
wiley   +1 more source

Fixed Point Results for Coupled Large Kannan Contraction Using W‐Distance and Its Application to Integral Equations

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In the present paper, we employ the notion of w‐distance to prove a large Kannan‐type contraction inequality in metric spaces. The notion of a coupled large Kannan contraction is introduced, and by using the Geraghty‐type control function, we derive fixed point results in metric spaces with and without partial order.
Priyam Chakraborty, Binayak S. Choudhury, Amaresh Kundu, Santosh Kumar, Ljubisa Kocinac   +4 more
wiley   +1 more source

Three-Step Fixed Point Iteration for Generalized Multivalued Mapping in Banach Spaces

Journal of Applied Mathematics, 2012
The convergence of three-step fixed point iterative processes for generalized multivalued nonexpansive mapping was considered in this paper. Under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to ...
Zhanfei Zuo
doaj   +1 more source

Convergence Behavior of the F∗ Algorithm: Strong and Weak Results for Nonexpansive Mappings

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study examines the strong and weak convergence of the F∗ iterative approach to the fixed point of a nonexpansive mapping in the context of a Banach space. This work shows improved rate and efficiency of convergence. Furthermore, we proved that F∗ iterative algorithm converges to a fixed point faster than Picard, Mann, S, and Varat iterative ...
Anju Panwar, Poonam Yadav, Mohammad Sajid, Ji Gao   +3 more
wiley   +1 more source

Fixed-Point Theorems for Mean Nonexpansive Mappings in Banach Spaces

Abstract and Applied Analysis, 2014
We define a mean nonexpansive mapping T on X in the sense that Tx-Ty≤ax-y+bx-Ty, a,b≥0,a+b≤1. It is proved that mean nonexpansive mapping has approximate fixed-point sequence, and, under some suitable conditions, we get some existence and uniqueness ...
Zhanfei Zuo
doaj   +1 more source

An Inertial Three‐Term Conjugate Gradient Projection Method With Applications

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper introduces a robust inertial three‐term projection method for solving monotone nonlinear equations. The proposed approach extends existing nonlinear conjugate gradient (CG) methods for unconstrained optimization with inexact line search by incorporating an inertial mechanism and a redesigned three‐term search direction to enhance numerical ...
Muhammad Abdullahi, Mohammed A. Saleh, Seyed Yaser Mousavi Siamakani, Abdulgader Z. Almaymuni, Auwal Bala Abubakar, Abubakar Sani Halilu, Sulaiman M. Ibrahim, Predrag S. Stanimirović   +7 more
wiley   +1 more source

Convergence of Monotone Generalized $\alpha$-nonexpansive Mappings in Ordered Hyperbolic Metric Spaces [PDF]

Sahand Communications in Mathematical Analysis
In this paper, we discuss SPK iterative algorithm for approximating fixed point of monotone generalized $\alpha$-nonexpansive mapping  in the setting of partially ordered hyperbolic spaces.
Samir Dashputre, Kavita Sakure
doaj   +1 more source

Iterative Schemes of Mean Nonexpansive Mapping

Journal of Harbin University of Science and Technology, 2021
Based on Mann iteration, Ishikawa iteration and some other twostep iteration, threestep iteration methods, two new fourstep iteration schemes and one nstep iteration are constructed.
CUI Yunan , ZHANG Jiaxing
doaj   +1 more source