scholarly journals Stability properties and asymptotic almost periodicity for linear Volterra difference equations in a Banach space

2005 ◽  
Vol 31 (2) ◽  
pp. 193-223 ◽  
Author(s):  
Satoru MURAKAMI ◽  
Yutaka NAGABUCHI
Keyword(s):  
Banach Space ◽  
Difference Equations ◽  
Almost Periodicity ◽  
Stability Properties ◽  
Volterra Difference Equations

Stabilities in Volterra difference equations on a Banach space

2004 ◽  
pp. 159-175 ◽  
Author(s):  
Tetsuo Furumochi ◽  
Satoru Murakami ◽  
Yutaka Nagabuchi
Keyword(s):  
Banach Space ◽  
Difference Equations ◽  
Volterra Difference Equations

scholarly journals Discrete Weighted Pseudo-Almost Automorphy and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhinan Xia
Keyword(s):  
Banach Space ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Convolution Type ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Volterra Difference Equations

We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings.

scholarly journals Asymptotic Almost-Periodicity for a Class of Weyl-Like Fractional Difference Equations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 592 ◽  
Author(s):  
Junfei Cao ◽  
Amar Debbouche ◽  
Yong Zhou
Keyword(s):  
Banach Space ◽  
Difference Equations ◽  
Existence Theorems ◽  
Mild Solutions ◽  
Almost Periodicity ◽  
Decomposition Technique ◽  
Fractional Difference ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Locally Lipschitz ◽  
Special Case

This work deal with asymptotic almost-periodicity of mild solutions for a class of difference equations with a Weyl-like fractional difference in Banach space. Based on a combination of a decomposition technique and the Krasnoselskii’s fixed point theorem, we establish some new existence theorems of mild solutions with asymptotic almost-periodicity. Our results extend some related conclusions, since (locally) Lipschitz assumption on the nonlinear perturbation is not needed and with Lipschitz assumption becoming a special case. An example is presented to validate the application of our results.

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