A new Krasnoselskii’s type algorithm for zeros of strongly monotone and Lipschitz mappings

For , let be a -uniformly smooth real Banach space with dual space . Let be a Lipschitz and strongly monotone mapping such that . For given , let be generated iteratively by the algorithm :

where is the normalized duality mapping from into
and is a positive real number choosen in a suitable interval. Then it is proved that the sequence converges strongly to , the unique point of . Our theorems are applied to the convex minimization problem. Futhermore, our technique of proof is of independent interest.