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.
UDOCHUKWU, O (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-1
UDOCHUKWU, OGBUISI "Strong Convergence Of Modified Averaging Iterative Algorithm For Asymptotically Nonexpansive Maps." Afribary. Afribary, 13 May. 2021, https://afribary.com/works/strong-convergence-of-modified-averaging-iterative-algorithm-for-asymptotically-nonexpansive-maps-1. Accessed 20 Apr. 2024.
UDOCHUKWU, OGBUISI . "Strong Convergence Of Modified Averaging Iterative Algorithm For Asymptotically Nonexpansive Maps.". Afribary, Afribary, 13 May. 2021. Web. 20 Apr. 2024. < https://afribary.com/works/strong-convergence-of-modified-averaging-iterative-algorithm-for-asymptotically-nonexpansive-maps-1 >.
UDOCHUKWU, OGBUISI . "Strong Convergence Of Modified Averaging Iterative Algorithm For Asymptotically Nonexpansive Maps." Afribary (2021). Accessed April 20, 2024. https://afribary.com/works/strong-convergence-of-modified-averaging-iterative-algorithm-for-asymptotically-nonexpansive-maps-1