In this paper, we propose a viscosity iteration process for semigroup of asymptotically pseudocontractive mappings, and prove a strong convergence theorem in uniformly convex Banach space for the proposed iteration process.

We construct adaptive Mann iterations for finding fixed points of strongly pseudocontractive mappings and solving nonlinear strongly accretive (not necessary continuous) operator equation Sx = f in p-smooth Banach spaces.

*Correspondence: [email protected] African University of Science and Technology, Abuja, Nigeria Abstract Let E be a real normed space with dual space E∗ and let A : E→ 2E be any map. Let J : E→ 2E be the normalized duality map on E. A new class of mappings, J-pseudocontractive maps, is introduced and the notion of J-fixed points is used to prove that T := (J – A) is J-pseudocontractive if an...

and Applied Analysis 3 literature. For some works related to the equilibrium problem, fixed point problems, and the variational inequality problem, please see 1–57 and the references therein. However, we note that all constructed algorithms in 7, 9–13, 16, 57 do not work to find the minimum-norm solution of the corresponding fixed point problems and the equilibrium problems. Very recently, Yao ...

We consider a mean value iteration for a family of functions, which corresponds to the Mann iteration with lim n→∞ α n = 0. We prove convergence results for this iteration when applied to strongly pseudocontractive or strongly accretive maps.