scholarly journals The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
M. O. Aibinu ◽  
S. C. Thakur ◽  
S. Moyo
Keyword(s):  
Necessary Conditions ◽  
Nonexpansive Mappings ◽  
Convergence Result ◽  
Nonlinear Operators ◽  
Asymptotically Nonexpansive Mappings ◽  
Convergence Results ◽  
Asymptotically Nonexpansive ◽  
Solving Equations ◽  
Computation Of Fixed Points ◽  
Iterative Procedures

The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotically nonexpansive mappings by the implicit midpoint iterative procedures. The necessary conditions for the convergence of the class of asymptotically nonexpansive mappings are established, by using a well-known iterative algorithm which plays important roles in the computation of fixed points of nonlinear mappings. A numerical example is presented to illustrate the convergence result. Under relaxed conditions on the parameters, some algorithms and strong convergence results were derived to obtain some results in the literature as corollaries.

scholarly journals Weak Convergence for Nonself Nearly Asymptotically Nonexpansive Mappings by Iterations

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
Safeer Hussain Khan
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Opial Condition ◽  
Asymptotically Nonexpansive Mappings ◽  
Convergence Results ◽  
Asymptotically Nonexpansive

AbstractIn this paper, we obtain a couple of weak convergence results for nonself nearly asymptotically nonexpansive mappings. Our first result is for the Banach spaces satisfying Opial condition and the second for those whose dual satisfies the Kadec-Klee property.

FIBONACCI–MANN ITERATION FOR MONOTONE ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

2017 ◽  
Vol 96 (2) ◽  
pp. 307-316 ◽  
Author(s):  
M. R. ALFURAIDAN ◽  
M. A. KHAMSI
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Convergence Result ◽  
Convex Banach Space ◽  
Opial Condition ◽  
Mann Iteration ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Nonempty Convex ◽  
Image Position

We extend the results of Schu [‘Iterative construction of fixed points of asymptotically nonexpansive mappings’, J. Math. Anal. Appl.158 (1991), 407–413] to monotone asymptotically nonexpansive mappings by means of the Fibonacci–Mann iteration process $$\begin{eqnarray}x_{n+1}=t_{n}T^{f(n)}(x_{n})+(1-t_{n})x_{n},\quad n\in \mathbb{N},\end{eqnarray}$$ where $T$ is a monotone asymptotically nonexpansive self-mapping defined on a closed bounded and nonempty convex subset of a uniformly convex Banach space and $\{f(n)\}$ is the Fibonacci integer sequence. We obtain a weak convergence result in $L_{p}([0,1])$, with $1<p<+\infty$, using a property similar to the weak Opial condition satisfied by monotone sequences.

scholarly journals Convergence Results for Proximal Point Algorithm in Complete Cat(0) Space for Multivalued Mappings

2021 ◽  
Vol 27 (1) ◽  
pp. 29-47
Author(s):  
Samir Dashputre ◽  
C. Padmavati ◽  
Kavita Sakure
Keyword(s):  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Multivalued Mappings ◽  
Proximal Point ◽  
Convergence Theorems ◽  
Numerical Example ◽  
Asymptotically Nonexpansive Mappings ◽  
Convergence Results ◽  
Asymptotically Nonexpansive

In this paper, we propose the modified proximal point algorithm with the process for three nearly Lipschitzian asymptotically nonexpansive mappings and multivalued mappings in CAT(0) space under certain conditions. We prove some convergence theorems for the algorithm which was introduced by Shamshad Hussain et al. [18]. A numerical example is given to illustrate the efficiency of proximal point algorithm for supporting our result.

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

scholarly journals Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yuanheng Wang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Real Banach Space ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Uniformly Gâteaux Differentiable Norm ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm

In the framework of a real Banach space with uniformly Gateaux differentiable norm, some new viscosity iterative sequences{xn}are introduced for an infinite family of asymptotically nonexpansive mappingsTii=1∞in this paper. Under some appropriate conditions, we prove that the iterative sequences{xn}converge strongly to a common fixed point of the mappingsTii=1∞, which is also a solution of a variational inequality. Our results extend and improve some recent results of other authors.

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