Asymptotic almost periodic functions with range in a topological vector space

The notion of asymptotic almost periodicity was first introduced by fréchet in 1941 in the case of finite dimensional range spaces. later,its extension to the case of banach range spaces and locally convex range spaces has been considered by several authors. in this paper,we have generalized the concept of asymptotic almost periodicity to the case where the range space is a general topological vector space,not necessarily locally convex. our results thus widen the scope of applications of asymptotic almost periodicity. © 2013 liaqat ali khan and saud m. alsulami.