Convergence of iterative algorithms for continuous pseudocontractive mappings

In this paper, we prove strong convergence of a path for a convex combination of a pseudocontractive type of operators in a real reflexive Banach space having a weakly continuous duality mapping J? with gauge function ?. Using path convergency, we establish strong convergence of an implicit iterative algorithm for a pseudocontractive mapping combined with a strongly pseudocontractive mapping in the same Banach space.

Viscosity Projection Algorithms for Pseudocontractive Mappings in Hilbert Spaces

An explicit projection algorithm with viscosity technique is constructed for finding the fixed points of the pseudocontractive mapping in Hilbert spaces. Strong convergence theorem is demonstrated. Consequently, as an application, we can approximate to the minimum-norm fixed point of the pseudocontractive mapping.

Iterative Methods for Pseudocontractive Mappings in Banach Spaces

LetEa reflexive Banach space having a uniformly Gâteaux differentiable norm. LetCbe a nonempty closed convex subset ofE,T:C→Ca continuous pseudocontractive mapping withF(T)≠∅, andA:C→Ca continuous bounded strongly pseudocontractive mapping with a pseudocontractive constantk∈(0,1). Let{αn}and{βn}be sequences in(0,1)satisfying suitable conditions and for arbitrary initial valuex0∈C, let the sequence{xn}be generated byxn=αnAxn+βnxn-1+(1-αn-βn)Txn, n≥1.If either every weakly compact convex subset ofEhas the fixed point property for nonexpansive mappings orEis strictly convex, then{xn}converges strongly to a fixed point ofT, which solves a certain variational inequality related toA.

New Iterative Manner Involving Sunny Nonexpansive Retractions for Pseudocontractive Mappings

Iterative methods for pseudocontractions have been studied by many authors in the literature. In the present paper, we firstly propose a new iterative method involving sunny nonexpansive retractions for pseudocontractions in Banach spaces. Consequently, we show that the suggested algorithm converges strongly to a fixed point of the pseudocontractive mapping which also solves some variational inequality.