Known as the father of modern analysis, Weierstrass devised tests for the convergence of series and contributed to the theory of periodic functions, functions of real variables, elliptic functions, Abelian functions, converging infinite products, and the calculus of variations.
Note that the space of almost periodic functions contains the space of periodic functions.
Sums of periodic functions are in the intersection of the classes of quasi-periodic functions and sums of semi-periodic functions.
Hence, when such functions, obtained by using a combination of periodic functions, are not periodic, they are not without properties: they are almost periodic functions.
Reversely, a uniformly convergent series of periodic functions is a.p.
Due to the presence of periodic functions in Eq. (10), the objective function contained large amounts of the local minima.
In fact, the first motivation for the study of almost periodic functions is the set of various ways to combine periodic functions with different periods.
In the first section, we study general almost periodic functions and asymptotically almost periodic ones.
In the literature several concepts have been studied to represent the idea of approximately periodic function (see [1]).
Then Zaidman [12] studied almost periodic functions from R N into a Banach space.
Studying periodic functions on ({mathbb R}^d) is equivalent to studying functions on the d-dimensional torus ({mathbb T}^d).
