Strong Convergence of Hybrid Approximate Proximal-Type Algorithm

Finding zero points for maximal monotone operator is a very active topic in different branches of mathematical and engineering sciences since many physically significant problems can be ultimately converted to it. Considerable research efforts have been devoted to the study of iterative algorithms of zero points for maximal monotone operators in recent years. By now, there already exist some algorithms, but they are not quite enough to deal with problems defined in a more general space. In this paper, a new hybrid approximate proximal-type algorithm is introduced which is proved to be strongly convergent to zero point of maximal monotone operator in Banach space by using some techniques of Lyapunov functional and generalized projection operator, etc. Moreover, the application of the new algorithm is demonstrated.