The generalized contraction proximal point algorithm with square-summable errors

Let (x_n) be a sequence generated by xn+1=αnu+γnxn+δnJβnxn+en for n≥ 0 , where Jβn is the resolvent of a maximal monotone operator A with β_n∈ (0 , ∞) , u, x₀∈ H, (e_n) is a sequence of errors and α_n∈ (0 , 1) , γ_n∈ (- 1 , 1) , δ_n∈ (0 , 2) are real numbers such that α_n+ γ_n+ δ_n= 1 for all n≥ 0. We present strong convergence results for the sequence generated by the generalized contraction proximal point algorithm defined above under weaker accuracy conditions and mild conditions on the parameters α_n, β_n and δ_n. Our results generalize and unify many known results in the literature.