Abstract
This paper is devoted to the study of the class of continuous and bounded functions f : [ 0 , ∞ ) → X for which exists ω > 0 such that lim t → ∞ ( f ( t + ω ) − f ( t ) ) = 0 (in the sequel called S-asymptotically ω-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically ω-periodic functions. We also study the existence of S-asymptotically ω-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces.
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