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Definition 6 We call ψ : [0, ∞) → [0, 1) a stronger Meir-Keeler function if the function ψ satisfies the following condition ∀ η > 0 ∃ δ > 0 ∃ γ η ∈ 0, 1 ∀ t ∈ 0, ∞ η ≤ t < δ + η ⇒ ψ t < γ η. The following provides an example of a stronger Meir-Keeler function. Example 3 Let ψ : ℝ + → 0, 1 be defined by ψ d x, y = 2 t 3 t + 1. Then ψ is a stronger Meir-Keeler function.
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