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The problem concerned in this paper is the set-valued equation 0 ∈ T(z) where T is a maximal monotone operator. For given xk and βk ＞ 0, some existing approximate proximal point algorithms take xk+1 = xk such that xk +ek∈ xk + βkT(xk) and||ek|| ≤ηk||xk -