Convergence of Ishikawa Iterates of Quasi-Nonexpansive Mappings

Abstract

This paper deals with a necessary and sufficient condition for the convergence of Ishikawa iterates of quasi-nonexpansive mapping in a Banach space. The convergence of Ishikawa iterates for nonexpansive mappings in a uniformly convex Banach space is also discussed. ᮊ 1997 Academic Press

Approximation of a common minimum-norm fixed point of a finite family of σ -asymptotically quasi-nonexpansive mappings with applications

“…it follows from (3.9), (3.10), (3.11) and the uniform continuity of T i that 12) as n → ∞ for each i = 1, 2, · · · , N . Let {v n k } be subsequence of {v n } such that lim sup…”

“…In 1997, Ghosh and Debnath [12] extended the results of [19] and gave a sufficient and necessary condition for Ishikawa iterative sequences to converge to fixed points for quasi-nonexpansive mappings. Using these, they have also obtained some sufficient conditions for Ishikawa iterative sequences converge to fixed points for nonexpansive mappings.…”

Approximation of Common Fixed Points of a Family of Asymptotically Quasi-Nonexpansive Mappings

“…Qihou [6] extended results of [1,5] and gave the necessary and sufficient conditions for Ishikawa iterative sequence to converge to fixed point of asymptotically quasi-nonexpansive mappings.…”

“…[4]) to converge to fixed points of quasi-nonexpansive mappings. In 1997, Ghosh and Debnath [1] extended the results of Petryshyn and Williamson [5] and gave necessary and sufficient conditions for Ishikawa iterative sequence to converge to fixed points for quasi-nonexpansive mappings.…”

Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces

“…Ghosh and Debnath [2] extended the result of [7] and gave a sufficient and necessary conditions for strong convergence of Ishikawa-type iteration process to a fixed point of a quasinonexpansive mapping in a real Banach space. Qihou [8] extended the resul of Ghosh and…”