IJPAM: Volume 79, No. 2 (2012)
THE CLASS OF WEAKLY ALMOST PERIODIC AND
PSEUDO ALMOST PERIODIC FUNCTIONS



Laboratory of Math Physics; Specials Functions and Applications
LR11ES35, Ecole Supérieure des Sciences et de Technologie
4002, Sousse, TUNISIA

Hammam-Sousse
4002, Sousse, TUNISIA
Abstract. In this paper we are concerned with the Eberlein's weakly almost periodic
functions. First, we shall use The Ryll-Nardzewski fixed point theorem to prove that
, the generalized mean in time, of a weakly
almost periodic function
is the unique common fixed point of the
operators of translation. Next, we give a generalization of a Besicovitch's
theorem for the class of weakly almost periodic functions and the class of
pseudo almost periodic functions. Next, we apply our result for the study of
some abstract differential equation.
Received: October 18, 2011
AMS Subject Classification: 42A75, 43A60, 42A16, 47H10
Key Words and Phrases: pseudo almost periodic functions, weakly almost periodic functions, fourier-Bohr series, fixed point theorems
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 2