Common Fixed Points Iteration Processes for a Finite Family of Asymptotically Nonexpansive Mappings
JuiโChi Huang ยท Georgian Mathematical Journal ยท 2004
Abstract Let ๐ธ be a uniformly convex Banach space which satisfies Opial's condition or its dual ๐ธ* has the KadecโKlee property, ๐ถ a nonempty closed convex subset of ๐ธ, and ๐๐ : ๐ถ โ ๐ถ an asymptotically nonexpansive mapping for each ๐ = 1, 2, . . . , ๐. Suppose {๐ฅ๐} is generated iteratively by where ๐๐(0) = ๐ผ, ๐ผ is the identity map and {ฮฑ ๐(๐)} is a suitable sequence in [0, 1]. If the set of common fixed points of is nonempty, then weak convergence of {๐ฅ๐} to some is obtained.