Weighted Stepanov-like pseudo almost automorphy and applications |
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Authors: | Zhinan Xia Meng Fan |
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Institution: | School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, PR China |
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Abstract: | In this paper, we propose a new class of functions called weighted Stepanov-like pseudo almost automorphic functions, which generalize in a natural fashion the concept of almost automorphy and its various extensions. We systematically explore the properties of the weighted Stepanov-like pseudo almost automorphic functions in general Banach space including a composition result. As an application, we establish some sufficient criteria for the existence, uniqueness of the weighted pseudo almost automorphic solution to a class of partial neutral functional differential equations and also to a class of nonlinear Volterra integral equations of convolution type with infinite delay in Banach space. Some interesting examples are presented to illustrate the main findings. |
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Keywords: | 92D25 39A11 37M05 |
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