A Generalization of Wiener's Lemma and its Application to Volterra Difference Equations on a Banach Space

2004 ◽  
Vol 10 (13-15) ◽  
pp. 1201-1214 ◽  
Author(s):  
Tetsuo Furumochi ◽  
Satoru Murakami ◽  
Yutaka Nagabuchi
Keyword(s):  
Banach Space ◽  
Difference Equations ◽  
Wiener’S Lemma ◽  
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.

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