On an application of the fixed-point principle in the theory of linear transformations of spaces with an indefinite metric

1955 ◽  
pp. 27-35 ◽  
Author(s):  
M. G. Kreĭn
Keyword(s):  
Fixed Point ◽  
Indefinite Metric ◽  
Linear Transformations ◽  
Fixed Point Principle

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.

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.

scholarly journals Controllability of Fractional Neutral Stochastic Integro-Differential Systems with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Xichao Sun ◽  
Litan Yan ◽  
Jing Cui
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Abstract Space ◽  
Differential Systems ◽  
Compactness Condition ◽  
Fixed Point Principle ◽  
Controllability Result

This paper is concerned with the controllability of a class of fractional neutral stochastic integro-differential systems with infinite delay in an abstract space. By employing fractional calculus and Sadovskii's fixed point principle without assuming severe compactness condition on the semigroup, a set of sufficient conditions are derived for achieving the controllability result.

On a fixed point principle of Sadovskii

1978 ◽  
Vol 2 (5) ◽  
pp. 643-645 ◽  
Author(s):  
S.J. Daher
Keyword(s):  
Fixed Point ◽  
Fixed Point Principle

scholarly journals Solutions to BSDEs Driven by Multidimensional Fractional Brownian Motions

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Jie Miao ◽  
Xu Yang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Conditional Expectation ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Fixed Point Principle ◽  
Fractional Ito Formula

We study more general backward stochastic differential equations driven by multidimensional fractional Brownian motions. Introducing the concept of the multidimensional fractional (or quasi-) conditional expectation, we study some of its properties. Using the quasi-conditional expectation and multidimensional fractional Itô formula, we obtain the existence and uniqueness of the solutions to BSDEs driven by multidimensional fractional Brownian motions, where a fixed point principle is employed. Finally, solutions to linear fractional backward stochastic differential equations are investigated.

THE FIXED-POINT PRINCIPLE

1982 ◽  
pp. 474-497 ◽  
Author(s):  
L.V. KANTOROVICH ◽  
G.P. AKILOV
Keyword(s):  
Fixed Point ◽  
Fixed Point Principle

An Application of B. N. Sadovskij’s Fixed Point Principle to Nonlinear Singular Equations

1987 ◽  
Vol 6 (3) ◽  
pp. 193-208 ◽  
Author(s):  
Jürgen Appell ◽  
Espedito De Pascale ◽  
Petr Zabrejko
Keyword(s):  
Fixed Point ◽  
Singular Equations ◽  
Fixed Point Principle

scholarly journals Existence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delays

2016 ◽  
Vol 16 (06) ◽  
pp. 1650014 ◽  
Author(s):  
Mamadou Abdoul Diop ◽  
Tomás Caraballo ◽  
Mahamat Mahamat Zene
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Resolvent Operators ◽  
Infinite Delays ◽  
Fixed Point Principle ◽  
Exponentially Stable

In this work we study the existence, uniqueness and asymptotic behavior of mild solutions for neutral stochastic partial integrodifferential equations with infinite delays. To prove the results, we use the theory of resolvent operators as developed by R. Grimmer [13], as well as a version of the fixed point principle. We establish sufficient conditions ensuring that the mild solutions are exponentially stable in [Formula: see text]th-moment. An example is provided to illustrate the abstract results.

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