LAUSR

Let $$(x_n)$$(xn) be a sequence generated by $$x_{n+1}=\alpha _nu+\gamma _nx_n+\delta _nJ_{\beta _n}x_n+e_n$$xn+1=αnu+γnxn+δnJβnxn+en for $$n\ge 0$$n≥0, where $$J_{\beta _n}$$Jβn is the resolvent of a maximal monotone operator A with $$\beta _n\in (0,\infty )$$βn∈(0,∞), $$u,x_0\in H$$u,x0∈H, $$(e_n)$$(en) is a sequence of errors and $$\alpha _n\in (0,1)$$αn∈(0,1), $$\gamma _n\in (-1,1)$$γn∈(-1,1), $$\delta _n\in (0,2)$$δn∈(0,2) are real numbers such that $$\alpha _n+\gamma _n+\delta _n=1$$αn+γn+δn=1 for all $$n\ge 0$$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 $$\alpha _n, \beta _n$$αn,βn and $$\delta _n$$δn. Our results generalize and unify many known results in the literature.