  This paper provides a new way of developing the splitting method which is
used to solve the problem of finding the resolvent of the sum of maximal
monotone operators in Hilbert spaces. By employing accelerated techniques
developed by Davis and Yin (in Set-Valued Var. Anal. 25(4):829-858, 2017), this
paper presents an implementable, strongly convergent splitting method which is
designed to solve the problem. In particular, we show that the distance between
the sequence of iterates and the solution converges to zero at a rate O(1/k) to
illustrate the efficiency of the proposed method, where k is the number of
iterations. Then, we apply the result to a class of optimization problems.
