Erratum to: "Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response" [Math. Comput. Modelling 49 (2009) 1829-1836]

Let ω > 0 be a constant. Suppose that {tk}∞k=−∞ is an increasing two-sided sequence and there exists a positive integer q such that tk+q = tk + ω for all k. Define PCω to be the space of all ω-periodic functions ψ : R→ R which are continuous for t 6= tk, are continuous from the left for t ∈ R and have possible discontinuities of the first kind at points t = tk; that is, the limit from the right of tk exists but may be different from the value at tk. For ψ ∈ PCω ,∆ψ(tk) = ψ(t k )− ψ(tk) is the jump at tk. Further, define PC1 ω = {ψ ∈ PCω : ψ is continuously differentiable on each (tk, tk+1]with ψ̇ ∈ PCω}. In [1], PC 1 ω is defined as PC1 ω = {ψ ∈ PCω : ψ̇ ∈ PCω}, which is the common definition in the literature. The latter definition is a little bit vague and this leads to the wrong claim thatψ is continuous ifψ ∈ PC1 ω . As a result, supt∈[0,ω] ψ(t) or inft∈[0,ω] ψ(t)may not be achieved at some t ∈ [0, ω]. Consequently, the proof of Lemma 3.1 [1] is not complete. The purpose of this note is to give a complete proof of the lemma.