Abstract
Abstract In this paper, a parallel iterative algorithm with mixed errors is investigated. Strong and weak convergence theorems of common fixed points of a finite family of strictly pseudocontractive mappings are established in a real Banach space. AMS Subject Classification:47H05, 47H09, 47J25.
Highlights
1 Introduction and preliminaries Throughout this paper, we denote by E and E∗ a real Banach space and a dual space of E, respectively
We show that is λ-strictly pseudocontractive mapping, where λ := min{λm : ≤ m ≤ N}
+ δ x – y – λ (I – T )x – (I – T )y + · · · + δN x – y – λN (I – TN )x – (I – TN )y ≤ x – y – λ δ (I – T )x – (I – T )y + δ (I – T )x – (I – T )y + · · · + δN (I – TN )x – (I – TN )y ≤ x – y – λ (I – T)x – (I – T)y. This proves that T is λ-strictly pseudocontractive mapping
Summary
[ ] Let {an}, {bn}, and {cn} be three nonnegative sequences satisfying the following condition: an+ ≤ ( + bn)an + cn, ∀n ≥ n , where n is some nonnegative integer,. Let E be a smooth and reflexive Banach space which satisfies Opial’s condition and K be a nonempty closed convex subset of E. Let N ≥ be some positive integer. N}, be a λi-strictly pseudocontractive mapping and {un} be a bounded sequence in K. Let {xn}∞ n= be a sequence generated in the following algorithm:. N ≥ , where {αn}, {βn}, {γn}, and {δm} are real number sequences in [ , ]. ∅, and the above control sequences satisfy the following restrictions:.
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