Fixed Point Theorems and Uniqueness of the Periodic Solution for the Hematopoiesis Models

and Applied Analysis 3 In order to prove that the sequence {xn} is a Cauchy sequence with respect to norm ‖·‖C, we introduce an equivalent norm and show that {xn} is a Cauchy sequence with respect to the new one. Basing on the condition H2 , we see that there are two positive constantsM and m such that m ≤ y t ≤ M for all t ∈ R. Define the new norm ‖ · ‖1 by ‖u‖1 sup { 1 y t ‖u t ‖E : t ∈ R } , u ∈ BC R,E . 2.5