Abstract
We introduce the notions of the asymptotic 𝒮ℳ𝒦‐sequence with respect to the stronger Meir‐Keeler cone‐type mapping ξ : int(P)∪{θ}→[0,1) and the asymptotic 𝒲ℳ𝒦‐sequence with respect to the weaker Meir‐Keeler cone‐type mapping ϕ : int(P)∪{θ} → int(P)∪{θ} and prove some common fixed point theorems for these two asymptotic sequences in cone metric spaces with regular cone P. Our results generalize some recent results.
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