Abstract
AbstractAn intermixed algorithm for two strict pseudo-contractions in Hilbert spaces have been presented. It is shown that the suggested algorithms converge strongly to the fixed points of two strict pseudo-contractions, independently. As a special case, we can find the common fixed points of two strict pseudo-contractions in Hilbert spaces.
Highlights
Let C be a nonempty closed convex subset of a real Hilbert space H with its inner product ·, · and norm · .Definition
If T is a nonexpansive mapping with Fix(T) = ∅ and {αn} satisfies the condition
[ ] who introduced the following Ishikawa algorithm: yn = ( – βn)xn + βnTxn, n ≥, xn+ = ( – αn)xn + αnTyn, where {αn} and {βn} are sequences in the interval [, ], T is a self-mapping of C, and the initial guess x ∈ C is selected arbitrarily. (Ishikawa’s algorithm can be viewed as a double-step Mann’s algorithm.) Ishikawa proved that his algorithm converges in norm to a fixed point of a Lipschitz pseudo-contraction T if {αn} and {βn} satisfy certain conditions and if T is compact
Summary
Let C be a nonempty closed convex subset of a real Hilbert space H with its inner product ·, · and norm · .Definition. Yao et al Fixed Point Theory and Applications (2015) 2015:206 following manner: xn+ = αnxn + ( – αn)Txn, n ≥ . If T is a nonexpansive mapping with Fix(T) = ∅ and {αn} satisfies the condition
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