Reduction approach to second order perturbed state-dependent sweeping process

2019 ◽  
Vol 28 (2) ◽  
Author(s):  
MUSTAPHA FATEH YAROU
Keyword(s):  
Fixed Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Sweeping Process ◽  
New Approach ◽  
Standard Methods ◽  
First Order ◽  
Finite Dimensional ◽  
Perturbed State ◽  
State Dependent

In this paper, we present a new approach to solving second order nonconvex perturbed sweeping process in finite dimensional setting. It consists in a reduction of the problem to a first order one without use of the standard methods of fixed point theory. The perturbation, that is the external force applied on the system is not necessary with bounded values.

Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution

2020 ◽  
pp. 1-23 ◽  
Author(s):  
T. Sathiyaraj ◽  
JinRong Wang ◽  
D. O'Regan
Keyword(s):  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Second Order ◽  
Delay Systems ◽  
Stochastic Delay ◽  
Finite Dimensional ◽  
Sine And Cosine Functions ◽  
Cosine Functions ◽  
Theoretical Results

Abstract In this paper, we study the controllability of second-order nonlinear stochastic delay systems driven by the Rosenblatt distributions in finite dimensional spaces. A set of sufficient conditions are established for controllability of nonlinear stochastic delay systems using fixed point theory, delayed sine and cosine matrices and delayed Grammian matrices. Furthermore, controllability results for second-order stochastic delay systems driven by Rosenblatt distributions via the representation of solution by delayed sine and cosine functions are presented. Finally, our theoretical results are illustrated through numerical simulation.

scholarly journals A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 512 ◽  
Author(s):  
Erdal Karapınar ◽  
Panda Kumari ◽  
Durdana Lateef
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nash Equilibria ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
New Approach ◽  
Correctness Of Programs

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f ( x ) = x . (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach.

scholarly journals Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces

1991 ◽  
Vol 4 (1) ◽  
pp. 47-69 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Index Theory ◽  
Point Theory ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Third Order ◽  
Nonnegative Solutions ◽  
Fixed Point Index Theory

In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

scholarly journals A new approach on coupled fixed point theory in JS-metric spaces

2019 ◽  
Vol 20 (1) ◽  
pp. 323-336 ◽  
Author(s):  
Tanusri Senapati ◽  
◽  
Lakshmi Kanta Dey ◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
New Approach

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.

scholarly journals On Some New Jungck–Fisher–Wardowski Type Fixed Point Results

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2048
Author(s):  
Jelena Vujaković ◽  
Eugen Ljajko ◽  
Slobodan Radojević ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Approach ◽  
Complete Metric Spaces

Many authors used the concept of F−contraction introduced by Wardowski in 2012 in order to define and prove new results on fixed points in complete metric spaces. In some later papers (for example Proinov P.D., J. Fixed Point Theory Appl. (2020)22:21, doi:10.1007/s11784-020-0756-1) it is shown that conditions (F2) and (F3) are not necessary to prove Wardowski’s results. In this article we use a new approach in proving that the Picard–Jungck sequence is a Cauchy one. It helps us obtain new Jungck–Fisher–Wardowski type results using Wardowski’s condition (F1) only, but in a way that differs from the previous approaches. Along with that, we came to several new contractive conditions not known in the fixed point theory so far. With the new results presented in the article, we generalize, extend, unify and enrich methods presented in the literature that we cite.

Delay perturbed state-dependent sweeping process

2014 ◽  
Vol 95 (2) ◽  
pp. 270-282 ◽  
Author(s):  
Tahar Haddad ◽  
Touma Haddad
Keyword(s):  
Sweeping Process ◽  
Perturbed State ◽  
State Dependent

scholarly journals Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Hernán R. Henríquez ◽  
Marcos Rabelo ◽  
Luciana Vale
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Cauchy Problems ◽  
Impulsive Conditions

In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness.

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