Abstract
In this paper, we consider the approximations of an iterative process for asymptotically k-strict pseudocontractive mappings in Hilbert spaces. Finally, we present some examples to study the rate of convergence.
Highlights
In this paper, we consider the approximations of an iterative process for asymptotically k-strict pseudocontractive mappings in Hilbert spaces
For an asymptotically k-strict pseudocontractive type mapping T with sequence {γn}, Ceng et al proved that the Mann iteration sequence converges weakly to a fixed point of T
Lemma . [ ] Let B be a nonempty subset of a Hilbert space H and T : B → B be an asymptotically k-strict pseudocontractive type mapping in the intermediate sense with sequence {γn}
Summary
Since limn→∞[( – βn,m)λ + βn,mρmμn] ≤ and limn→∞ βn,m(ρmηn + σm) = , by Lemma . ), lim supn→∞ xn,m – q ≤ h, by inequality + σm , ρm h ≤ lim infn→∞ xn,m – q and limn→∞ xn,m – q = h. ), limn→∞ Tinxn,i – q ≤ h, by Lemma . Limn→∞ xn – Tin– xn,i– = for i = , . Φ(s)un ds – q ≤ ρ xn – q + σ , and limn→∞ n – q ≤ h and by Lemma . M – , limn→∞ βn,m = and βn,m the sequence. Since limn→∞ βn,m = and limn→∞ βn,m(ρmηn + σm) = , by Lemma .
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