scholarly journals About the Stabilization of a Nonlinear Perturbed Difference Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Slight Modification ◽  
Unmodeled Dynamics ◽  
Nonlinear Difference Equations ◽  
Oscillatory Solutions ◽  
Fixed Point Principle ◽  
Single Controller ◽  
Different Order

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

Construction of fixed point operators for nonlinear difference equations of non integer order with impulses

2020 ◽  
Vol 23 (3) ◽  
pp. 886-907
Author(s):  
Syed Sabyel Haider ◽  
Mujeeb Ur Rehman
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Nonlinear Difference Equations ◽  
Fractional Difference ◽  
Integer Order ◽  
Fractional Difference Equation ◽  
Point Operator

AbstractIn this article, we establish a technique for transforming arbitrary real order delta difference equations with impulses to corresponding summation equations. The technique is applied to non-integer order delta difference equation with some boundary conditions. Furthermore, the summation formulation for impulsive fractional difference equation is utilized to construct fixed point operator which in turn are used to discuss existence of solutions.

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

scholarly journals Fixed Points of the Evacuation of Maximal Chains on Fuss Shapes

10.37236/6898 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Sen-Peng Eu ◽  
Tung-Shan Fu ◽  
Hsiang-Chun Hsu ◽  
Yu-Pei Huang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Hasse Diagram ◽  
Linear Extensions ◽  
Rectangular Shape ◽  
Explicit Characterization ◽  
Finite Poset ◽  
Maximal Chains

For a partition $\lambda$ of an integer, we associate $\lambda$ with a slender poset $P$ the Hasse diagram of which resembles the Ferrers diagram of $\lambda$. Let $X$ be the set of maximal chains of $P$. We consider Stanley's involution $\epsilon:X\rightarrow X$, which is extended from Schützenberger's evacuation on linear extensions of a finite poset. We present an explicit characterization of the fixed points of the map $\epsilon:X\rightarrow X$ when $\lambda$ is a stretched staircase or a rectangular shape. Unexpectedly, the fixed points have a nice structure, i.e., a fixed point can be decomposed in half into two chains such that the first half and the second half are the evacuation of each other. As a consequence, we prove anew Stembridge's $q=-1$ phenomenon for the maximal chains of $P$ under the involution $\epsilon$ for the restricted shapes.

Some variants of Ćirić’s multi-valued contraction principle

2019 ◽  
Vol 57 (1) ◽  
pp. 23-42
Author(s):  
Cristian Daniel Alecsa ◽  
Adrian Petruşel
Keyword(s):  
Fixed Point ◽  
Fixed Point Problem ◽  
Contraction Principle ◽  
Point Problem ◽  
Strict Fixed Point ◽  
Fixed Point Principle

Abstract In this article, a study of the fixed point problem for Ćirić type multi-valued operators is presented. More precisely, some variants ofĆirić’s contraction principle for multi-valued operators, as well as a strict fixed point principle forĆirić type multi-valued will be given.

Verification of Iterative Methods for the Linear Complementarity Problem

2016 ◽  
pp. 545-580 ◽  
Author(s):  
H. Saberi Najafi ◽  
S. A. Edalatpanah
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Linear Complementarity Problem ◽  
Numerical Experiments ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Convergence Results ◽  
Fixed Point Principle ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

In the present chapter, we give an overview of iterative methods for linear complementarity problems (abbreviated as LCPs). We also introduce these iterative methods for the problems based on fixed-point principle. Next, we present some new properties of preconditioned iterative methods for solving the LCPs. Convergence results of the sequence generated by these methods and also the comparison analysis between classic Gauss-Seidel method and preconditioned Gauss-Seidel (PGS) method for LCPs are established under certain conditions. Finally, the efficiency of these methods is demonstrated by numerical experiments. These results show that the mentioned models are effective in actual implementation and competitive with each other.

A Characterization of the Compound-Exponential Type Distributions

2011 ◽  
Vol 54 (3) ◽  
pp. 464-471
Author(s):  
Tea-Yuan Hwang ◽  
Chin-Yuan Hu
Keyword(s):  
Fixed Point ◽  
Exponential Type ◽  
Existence And Uniqueness ◽  
Fixed Point Equation ◽  
Point Equation

AbstractIn this paper, a fixed point equation of the compound-exponential type distributions is derived, and under some regular conditions, both the existence and uniqueness of this fixed point equation are investigated. A question posed by Pitman and Yor can be partially answered by using our approach.

A Characterization of the Hughes Planes

1965 ◽  
Vol 17 ◽  
pp. 916-922 ◽  
Author(s):  
T. G. Ostrom
Keyword(s):  
Fixed Point ◽  
Projective Plane ◽  
Related Notion ◽  
Fixed Line

Baer (1) introduced the term "(p,L)-collineation" to denote a central collineation with centre p and axis L. We shall find it convenient to use a modification of the related notion of "(p, L)-transitivity."Definition. Let π0 be a subplane of the projective plane π. Let L be a fixed line of π0, and let p be a fixed point of π0. Let r and s be any two points of π0 that are collinear with p, distinct from p, and not on L. If, for each such choice of r and s, there is a (p, L)-collineation of π that (1) carries π0 into itself and (2) carries r into s, we shall say that π is (p, L, π0)-transitive.

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