Inexact Linearization of Fixed Point Iterations in the Piggy-Back Iterations of the One-Shot Adjoint

2022 ◽  
Author(s):  
Emmett Padway ◽  
Dimitri J. Mavriplis
Keyword(s):  
Fixed Point ◽  
The One ◽  
Fixed Point Iterations

Fractal Top for Contractive and Non-Contractive Transformations

2012 ◽  
Vol 3 (4) ◽  
pp. 49-65
Author(s):  
Sarika Jain ◽  
S. L. Singh ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Iterated Function System ◽  
Function System ◽  
Feedback Process ◽  
Iterated Function ◽  
Spatial Part ◽  
One Step ◽  
The One ◽  
Definition Of

Barnsley (2006) introduced the notion of a fractal top, which is an addressing function for the set attractor of an Iterated Function System (IFS). A fractal top is analogous to a set attractor as it is the fixed point of a contractive transformation. However, the definition of IFS is extended so that it works on the colour component as well as the spatial part of a picture. They can be used to colour-render pictures produced by fractal top and stealing colours from a natural picture. Barnsley has used the one-step feed- back process to compute the fractal top. In this paper, the authors introduce a two-step feedback process to compute fractal top for contractive and non-contractive transformations.

A Note on "Implicit Mann Fixed Point Iterations for Pseudo-Contractive Mappings"

2011 ◽  
Vol 393-395 ◽  
pp. 543-545
Author(s):  
Hong Jun Li ◽  
Yong Fu Su
Keyword(s):  
Fixed Point ◽  
Convergence Theorem ◽  
Nonempty Subset ◽  
Applied Mathematics ◽  
Iteration Process ◽  
Implicit Iteration Process ◽  
Contractive Mappings ◽  
Contractive Map ◽  
Fixed Point Iterations ◽  
Implicit Iteration

Ljubomir Ciric, Arif Rafiq, Nenad Cakic, Jeong Sheok Umed [ Implicit Mann fixed point iterations for pseudo-contractive mappings, Applied Mathematics Letters 22 (2009) 581-584] introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the relatively convergence theorem. However, the content of mann theorem is fuzzy. In this paper, we will give some comments . Let be a Banach space and be a nonempty subset of . A mapping is called hemi-contractive (see [1]) if and In [1], the authors introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the following convergence theorem.

scholarly journals Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 681-690
Author(s):  
Khairul Saleh ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Fixed Point Iterations

Abstract In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$ C A T 0 spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.

scholarly journals Anderson Acceleration for Fixed-Point Iterations

2011 ◽  
Vol 49 (4) ◽  
pp. 1715-1735 ◽  
Author(s):  
Homer F. Walker ◽  
Peng Ni
Keyword(s):  
Fixed Point ◽  
Anderson Acceleration ◽  
Fixed Point Iterations

scholarly journals IX. Remarks concerning the Natural-Historical Determination of Diallage

1826 ◽  
Vol 10 (1) ◽  
pp. 127-147
Author(s):  
W. Haidinger
Keyword(s):  
Fixed Point ◽  
Natural History ◽  
Distinct Species ◽  
The Other ◽  
Accurate Information ◽  
External Appearance ◽  
Slight Degree ◽  
The One

The following paper contains the results of a series of inquiries, which lead to the conclusion, that the mineral called Smaragdite by Saussure, does not form a species of its own; but that this name has been given to a compound of certain varieties of two distinct species, Augite and Hornblende, the natural-historical species of paratomous and hemiprismatic Augite-spar.Owing in part to the slight degree of resemblance prevailing among its varieties, the authors who have described them differ so essentially in opinion, that I am obliged to go into various details, both respecting the external appearance of the mineral itself, and of the opinions of mineralogists, in order to afford a correct view of the natural-historical species, to which these varieties belong, since this is the basis upon which every system, and, indeed, all accurate information in natural history, is founded, and the fixed point to which the one and the other must be referred.

scholarly journals On analytical and numerical study of implicit fixed point iterations

2015 ◽  
Vol 2 (1) ◽  
pp. 1021623
Author(s):  
Renu Chugh ◽  
Preety Malik ◽  
Vivek Kumar
Keyword(s):  
Fixed Point ◽  
Numerical Study ◽  
Fixed Point Iterations
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