A Viscosity Approximation Method with a Weakly Contractive Mapping of General Iterative Processes for Nonexpansive Semigroups in Banach Spaces

The general iterative methods for nonexpansive semigroups in Banach spaces

Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E∗. Let S {T s : 0 ≤ s < ∞} be a nonexpansive semigroup on E such that Fix S : ⋂t≥0Fix T t / ∅, and f is a contraction on E with coefficient 0 < α < 1. Let F be δ-strongly accretive and λ-strictly pseudocontractive with δ λ > 1 and γ a positive real number such that γ < 1/α 1 − √ 1 − δ...

A new viscosity approximation method for common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in Banach spaces

By use of a new viscosity approximation method, we construct an explicit iterative algorithm for finding common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in the framework of Banach spaces. A strong convergence theorem is obtained for solving a kind of variational inequality problems. Our results improve and extend the corresponding ones of other author...

A New Composite General Iterative Scheme for Nonexpansive Semigroups in Banach Spaces

Throughout this paper we denoted by and the set of all positive integers and all positive real numbers, respectively. Let X be a real Banach space, and let C be a nonempty closed convex subset ofX. Amapping T ofC into itself is said to be nonexpansive if ‖Tx−Ty‖ ≤ ‖x−y‖ for each x, y ∈ C. We denote by F T the set of fixed points of T . We know that F T is nonempty ifC is bounded; for more detai...

A General Iterative Algorithm for Nonexpansive Mappings in Banach Spaces

Let E be a real q-uniformly smooth Banach space whose duality map is weakly sequentially continuous. Let T : E → E be a nonexpansive mapping with F (T ) 6= ∅. Let A : E → E be an η-strongly accretive map which is also κ-Lipschitzian. Let f : E → E be a contraction map with coefficient 0 < α < 1. Let a sequence {yn} be defined iteratively by y0 ∈ E, yn+1 = αnγf(yn) + (I − αnμA)Tyn, n ≥ 0, where ...

A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions