Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space

Abstract EN

Let C be a nonempty closed and convex subset of a Hilbert space H, let T and S:C→C be two commutative generalized asymptotically nonexpansive mappings.

We introduce an implicit iteration process of S and T defined by xn=αnx0+(1−αn)(2/((n+1)(n+2)))∑k=0n∑i+j=kSiTjxn, and then prove that {xn} converges strongly to a common fixed point of S and T.

The results generalize and unify the corresponding results.