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

Abstract

"For q > 1, let E be a q-uniformly smooth real Banach space with dual space E∗. Let A : E → E∗ be a Lipschitz and strongly monotone mapping such that A^{−1}(0) ̸= ∅. For given x_1 ∈ E, let {x_n} be generated iteratively by the algorithm : x_{n+1} = x_n − λJ^{−1}(Ax_n), n ≥ 1, where J is the normalized duality mapping from E into E∗ and λ is a positive real number choosen in a suitable interval. Then it is proved that the sequence {xn} converges strongly to x∗, the unique point of A^{−1}(0). Our theorems are applied to the convex minimization problem. Futhermore, our technique of proof is of independent interest."