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

강신민|엄정석|Zeqing Liu
한국수학교육학회|2004.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제11권 제4호|pp. 293-308

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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.

참고문헌 (29)

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관련 논문AI추천

Almost stability of the Mann iteration method with errors for strictly hemi-contractive operators in smooth Banach spaces강신민, 심수학, Z. Liu대한수학회 · 대한수학회지2003 · 제40권 제1호Almost stability of Ishikawa iterative schemes with errors for $\phi$-strongly quasi-accretive and $\phi$-hemicontractive operatorsJong Kyu Kim, Shin Min Kang, Zeqing Liu대한수학회 · 대한수학회논문집2004 · 제19권 제2호Ishikawa Iterative Process with Errors for Strongly Pseudo-contractive Mappings in Banach SpacesYongjin Li대한수학회 · 대한수학회논문집2004 · 제19권 제3호Convergence theorems and stability problems of the modified Ishikawa iterative sequences for strictly successively hemicontractive mappings김기홍, 김종규, Zeqing Liu대한수학회 · 대한수학회보2002 · 제39권 제3호Necessary and sufficient conditions for convergence of Ishikawa iterative schemes with errors to $\phi$-hemicontractive mappingsJong Kyu Kim, Shin Min Kang, Zeqing Liu대한수학회 · 대한수학회논문집2003 · 제18권 제2호Modified Ishikawa Iterative sequences with errors for asymptotically set-valued pseudocontractive mappings in Banach Spaces김종규, 남영만대한수학회 · 대한수학회보2006 · 제43권 제4호

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