scholarly journals Positive Solutions and Mann Iterative Algorithms for a Nonlinear Three-Dimensional Difference System

2014 ◽  
Vol 2014 ◽  
pp. 1-23
Author(s):  
Zeqing Liu ◽  
Yan Lu ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Three Dimensional ◽  
Iterative Algorithms ◽  
Banach Fixed Point Theorem ◽  
Difference System

The existence of uncountably many positive solutions and Mann iterative approximations for a nonlinear three-dimensional difference system are proved by using the Banach fixed point theorem. Four illustrative examples are also provided.

scholarly journals Positive Solutions and Iterative Approximations for a Nonlinear Two-Dimensional Difference System with Multiple Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-57
Author(s):  
Zeqing Liu ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Error Estimates ◽  
Positive Solutions ◽  
Iterative Algorithms ◽  
Banach Fixed Point Theorem ◽  
Multiple Delays ◽  
Two Dimensional ◽  
Difference System ◽  
Analysis Techniques

This paper studies the nonlinear two-dimensional difference system with multiple delaysΔ(xn+p1nxn-τ1)+f1(n,xa1n,…,xahn,yb1n,…,ybkn)=q1n,Δ(yn+p2nyn-τ2)+f2(n,xc1n,…,xchn,yd1n,…,ydkn)=q2n,n≥n0. Using the Banach fixed point theorem and a few new analysis techniques, we show the existence of uncountably many bounded positive solutions for the system, suggest Mann iterative algorithms with errors, and discuss the error estimates between the positive solutions and iterative sequences generated by the Mann iterative algorithms. Examples to illustrates the results are included.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

scholarly journals Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui-Sheng Ding ◽  
Julio G. Dix
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type System ◽  
Functional Difference ◽  
Difference System ◽  
Multiple Periodic Solutions

This paper is concerned with the existence of multiple periodic solutions for discrete Nicholson’s blowflies type system. By using the Leggett-Williams fixed point theorem, we obtain the existence of three nonnegative periodic solutions for discrete Nicholson’s blowflies type system. In order to show that, we first establish the existence of three nonnegative periodic solutions for then-dimensional functional difference systemyk+1=Akyk+fk, yk-τ, k∈ℤ, whereAkis not assumed to be diagonal as in some earlier results. In addition, a concrete example is also given to illustrate our results.

scholarly journals Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang Liu ◽  
Zhang Weiguo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Boundary Value ◽  
Order Derivative ◽  
Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

scholarly journals Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

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