Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales

and Applied Analysis 3 A function p : T → R is called regressive provided 1 μ t p t / 0 for all t ∈ T. The set of all regressive and rd-continuous functions p : T → R will be denoted by R R T R T,R . We define the set R R T,R {p ∈ R : 1 μ t p t > 0, for all t ∈ T}. An n × n-matrix-valued function A on a time scale T is called regressive provided I μ t A t is invertible ∀t ∈ T, 2.4 and the class of all such regressive and rd-continuous functions is denoted, similar to the above scalar case, by R R T R T,Rn×n . If r is a regressive function, then the generalized exponential function er is defined by