We investigate the convergence analysis of the following general inexact algorithm for approximating a zero of the sum of a cocoercive operator and maximal monotone operators with : , for for given in a real Hilbert space , where , , and are sequences in with for all , denotes the error sequence, and is a contraction. The algorithm is known to converge under the following assumptions on and : (i) is bounded below away from 0 and above away from 1 and (ii) is summable in norm. In this paper, we show that these conditions can further be relaxed to, respectively, the following: (i) is bounded below away from 0 and above away from 3/2 and (ii) is square summable in norm; and we still obtain strong convergence results.
"The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators." Abstr. Appl. Anal. 2016 1 - 10, 2016. https://doi.org/10.1155/2016/2371857