ABSTRACT
Let H be a real Hilbert space and K a nonempty, closed and convex subset of H. Let
T : K ! K be an asymptotically nonexpansive map with a nonempty xed points set.
Let fng1n
=1 and ftng1 n=1 be real sequences in (0,1). Let fxng be a sequence generated
from an arbitrary x0 2 K by
yn = PK[(1 tn)xn]; n 0
xn+1 = (1 n)yn + nTnyn; n 0:
where PK : H ! K is the metric projection. Under some appropriate mild conditions
on fng1n
=1 and ftng1 n=1, we prove that fxng converges strongly to xed point of T. No
compactness assumption is imposed on T and or K and no further requirement is imposed
on the xed point set Fix(T) of T.
, O & UDOCHUKWU, F (2021). Strong Convergence Of Modified Averaging Iterative Algorithm For Asymptotically Nonexpansive Maps. Afribary. Retrieved from https://afribary.com/works/strong-convergence-of-modified-averaging-iterative-algorithm-for-asymptotically-nonexpansive-maps
, OGBUISI and FERDINARD UDOCHUKWU "Strong Convergence Of Modified Averaging Iterative Algorithm For Asymptotically Nonexpansive Maps" Afribary. Afribary, 05 May. 2021, https://afribary.com/works/strong-convergence-of-modified-averaging-iterative-algorithm-for-asymptotically-nonexpansive-maps. Accessed 06 May. 2024.
, OGBUISI, FERDINARD UDOCHUKWU . "Strong Convergence Of Modified Averaging Iterative Algorithm For Asymptotically Nonexpansive Maps". Afribary, Afribary, 05 May. 2021. Web. 06 May. 2024. < https://afribary.com/works/strong-convergence-of-modified-averaging-iterative-algorithm-for-asymptotically-nonexpansive-maps >.
, OGBUISI and UDOCHUKWU, FERDINARD . "Strong Convergence Of Modified Averaging Iterative Algorithm For Asymptotically Nonexpansive Maps" Afribary (2021). Accessed May 06, 2024. https://afribary.com/works/strong-convergence-of-modified-averaging-iterative-algorithm-for-asymptotically-nonexpansive-maps