Fixed Point Computation by Exponentiating Linear Operators

2019 ◽  
Author(s):  
Asma Mansouri ◽  
Matthieu Martel ◽  
Oana Silvia Serea
Keyword(s):  
Fixed Point ◽  
Linear Operators ◽  
Fixed Point Computation

scholarly journals Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-Han Zhao ◽  
Yong-Kui Chang ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Integrodifferential Equation ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Linear Operators ◽  
Asymptotic Behavior Of Solutions ◽  
Almost Automorphic ◽  
Partial Integrodifferential Equation

The existence of asymptotically almost automorphic mild solutions to an abstract stochastic fractional partial integrodifferential equation is considered. The main tools are some suitable composition results for asymptotically almost automorphic processes, the theory of sectorial linear operators, and classical fixed point theorems. An example is also given to illustrate the main theorems.

scholarly journals Relative controllability of a stochastic system using fractional delayed sine and cosine matrices

2021 ◽  
Vol 26 (6) ◽  
pp. 1031-1051
Author(s):  
JinRong Wang ◽  
T. Sathiyaraj ◽  
Donal O’Regan
Keyword(s):  
Fixed Point ◽  
Stochastic System ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Point Theory ◽  
Linear Operators ◽  
Relative Controllability ◽  
Finite Dimensional ◽  
Pure Delay

In this paper, we study the relative controllability of a fractional stochastic system with pure delay in finite  dimensional stochastic spaces. A set of sufficient conditions is obtained for relative exact controllability using fixed point theory, fractional calculus (including fractional delayed linear operators and Grammian matrices) and local assumptions on nonlinear terms. Finally, an example is given to illustrate our theory.

Using Digitised X-Ray Powder Diffraction Scans as Input for a New Pc-At Search/Match Program

1987 ◽  
Vol 31 ◽  
pp. 423-430 ◽  
Author(s):  
P. Caussin ◽  
J. Nusinovici ◽  
D.W. Beard
Keyword(s):  
Fixed Point ◽  
Data Base ◽  
Powder Diffraction ◽  
Phase Identification ◽  
Interactive Graphics ◽  
List Type ◽  
Fast Method ◽  
X Ray ◽  
Fixed Point Computation ◽  
Peak Location

AbstractA Search/Matcti program lias 'beea written for the IBM PC AT computer that is capable of -using "background - subtracted, digitized 2-ray powder diffraction scans as inputs in addition to the d/I data traditionally used. This novel procedure has proved especially effective when numerous unresolved lines are present in the pattern. The method is also less demanding of data quality thaii the peak location programs. The program may he extended to searching & data "base of digitized standard patterns.The program, has several parameters that can- "be adjusted, including chemistry. The results from the Johnson/Vand list type of output are directly accessible to the interactive graphics program. This gives the diffraction!st a fast method for verifying the phase identification. Because of the speed of fixed point computation techniques, the 52,791 pattern file can be scanned in about 90 seconds.This paper will illustrate the utility of the program.

scholarly journals Derivation tree analysis for accelerated fixed-point computation

2011 ◽  
Vol 412 (28) ◽  
pp. 3226-3241 ◽  
Author(s):  
Javier Esparza ◽  
Stefan Kiefer ◽  
Michael Luttenberger
Keyword(s):  
Fixed Point ◽  
Derivation Tree ◽  
Tree Analysis ◽  
Fixed Point Computation

scholarly journals Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Rudong Chen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Minimum Norm ◽  
Practical Applications ◽  
Fixed Point Computation ◽  
The Common ◽  
Special Case

Fixed point (especially, the minimum norm fixed point) computation is an interesting topic due to its practical applications in natural science. The purpose of the paper is devoted to finding the common fixed points of an infinite family of nonexpansive mappings. We introduce an iterative algorithm and prove that suggested scheme converges strongly to the common fixed points of an infinite family of nonexpansive mappings under some mild conditions. As a special case, we can find the minimum norm common fixed point of an infinite family of nonexpansive mappings.

scholarly journals On Second-Order Differential Equations with Nonsmooth Second Member

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
M. Milla Miranda ◽  
A. T. Lourêdo ◽  
L. A. Medeiros
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Initial Value Problem ◽  
Positive Function ◽  
Linear Operators ◽  
Initial Value ◽  
Second Order Differential Equations ◽  
Open Question ◽  
Abstract Framework

In an abstract framework, we consider the following initial value problem: u′′ + μAu + F(u)u = f  in  (0,T), u(0)=u0,u′(0)=u1, where μ is a positive function and f a nonsmooth function. Given u0, u1, and f we determine Fu in order to have a solution u of the previous equation. We analyze two cases of Fu. In our approach, we use the Theory of Linear Operators in Hilbert Spaces, the compactness Aubin-Lions Theorem, and an argument of Fixed Point. One of our two results provides an answer in a certain sense to an open question formulated by Lions in (1981, Page 284).

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