Convergence and Almost Stability of Ishikawa Iteration Method with Errors for Strictly Hemi-Contractive Operators in Banach Spaces

다국어 초록 (Multilingual Abstract)

Let K be a nonempty convex subset of an arbitrary Banach space
X and T : K ! K be a uniformly continuous strictly hemi-contractive operator
with bounded range. We prove that certain Ishikawa iteration scheme with errors
both converges strongly to a unique ¯xed point of T and is almost T-stable on K.
We also establish similar convergence and almost stability results for strictly hemi-
contractive operator T : K ! K, where K is a nonempty convex subset of arbitrary
uniformly smooth Banach space X. The convergence results presented in this paper
extend, improve and unify the corresponding results in Chang [1], Chang, Cho, Lee
& Kang [2], Chidume [3, 4, 5, 6, 7, 8], Chidume & Osilike [9, 10, 11, 12], Liu [19],
Schu [25], Tan & Xu [26], Xu [28], Zhou [29], Zhou & Jia [30] and others.

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