On semi-c-periodic functions of type I and applications
Keywords:
C-periodic; Semi-c-periodic; Uniformly close c-periodic; Volterra integral equation; Banach fixed point principleAbstract
In this paper, we study the (newly introduced) class of functions called semi-c-periodic functions of type I in a Banach space. We first investigate their basic properties, including a convolution result. Using a suitable norm we prove that the set of such functions is a Banach space. We then study the existence and uniqueness of semi-c-periodic mild solutions for both autonomous and non-autonomous linear evolution equations. We achieve the existence results using the Banach fixed point theorem and the principle of reduction
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