Remarks on Generalized Stability for Difference Equations in Banach Spaces

2018 ◽  
Vol 70 ◽  
pp. 77-82
Author(s):  
Ioan-Lucian Popa ◽  
Larisa Elena Biriş ◽  
Traian Ceauşu ◽  
Tongxing Li
Keyword(s):  
Banach Spaces ◽  
Difference Equations ◽  
Generalized Stability

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

The antipodal mapping theorem and difference equations in Banach spaces†

2005 ◽  
Vol 11 (12) ◽  
pp. 1037-1047 ◽  
Author(s):  
Daniel Franco ◽  
Donal O'Regan ◽  
Juan Peran
Keyword(s):  
Banach Spaces ◽  
Difference Equations

scholarly journals Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-qiu Song ◽  
Tian Yue ◽  
Dong-qing Li
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Time Systems

The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces. Well-known results for exponential stability and exponential dichotomy are extended to the case of nonuniform exponential trichotomy.

scholarly journals Exponential dichotomies for linear discrete-time systems in Banach spaces

2012 ◽  
Vol 6 (1) ◽  
pp. 140-155 ◽  
Author(s):  
Ioan-Lucian Popa ◽  
Mihail Megan ◽  
Traian Ceauşu
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Linear Difference Equations ◽  
Exponential Dichotomies ◽  
Discrete Time Systems ◽  
Time Systems

In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. Characterizations of these concepts are given. Some illustrating examples clarifies the relations between these concepts.

Impulsive Implicit Caputo Fractional q-Difference Equations in Finite- and Infinite-Dimensional Banach Spaces

2021 ◽  
pp. 187-209
Author(s):  
Badr Alqahtani ◽  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Gaston M. N’Guérékata
Keyword(s):  
Banach Spaces ◽  
Difference Equations ◽  
Infinite Dimensional

scholarly journals Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

2005 ◽  
Vol 2005 (17) ◽  
pp. 2769-2774
Author(s):  
Anna Kisiolek ◽  
Ireneusz Kubiaczyk
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Banach Spaces ◽  
Difference Equations ◽  
Measure Of Noncompactness ◽  
Nonlinear Difference Equations ◽  
Measure Of Weak Noncompactness ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

We consider the second-order nonlinear difference equations of the formΔ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution(xn), which possesses the asymptotic behaviour‖xn−a∑j=0n−1(1/rj)+b‖=o(1),a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose thatfhas values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.

Regularity of Difference Equations on Banach Spaces

2014 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Claudio Cuevas ◽  
Carlos Lizama
Keyword(s):  
Banach Spaces ◽  
Difference Equations
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