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ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERRORS FOR NONLINEAR $Phi$-STRONGLY QUASI-ACCRETIVE MAPPINGS IN NORMED LINEAR SPACES
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  • ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERRORS FOR NONLINEAR $Phi$-STRONGLY QUASI-ACCRETIVE MAPPINGS IN NORMED LINEAR SPACES
  • ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERRORS FOR NONLINEAR $Phi$-STRONGLY QUASI-ACCRETIVE MAPPINGS IN NORMED LINEAR SPACES
저자명
Zhou. H.Y.,Cho. Y.J.
간행물명
Journal of the Korean Mathematical Society
권/호정보
1999년|36권 6호|pp.1061-1073 (13 pages)
발행정보
대한수학회
파일정보
정기간행물|ENG|
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이 논문은 한국과학기술정보연구원과 논문 연계를 통해 무료로 제공되는 원문입니다.
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기타언어초록

Let X be a real normed linear space. Let T : D(T) ⊂ X longrightarrow X be a uniformly continuous and ∮-strongly quasi-accretive mapping. Let {${alpha}$n}{{{{ { }`_{n=0 } ^{$infty$ } }}}} , {${eta}$n}{{{{ { }`_{n=0 } ^{$infty$ } }}}} be two real sequences in [0, 1] satisfying the following conditions: (ⅰ) ${alpha}$n longrightarrow0, ${eta}$n longrightarrow0, as n longrightarrow$infty$ (ⅱ) {{{{ SUM from { { n}=0} to inf }}}} ${alpha}$=$infty$. Set Sx=x-Tx for all x $in$D(T). Assume that {u}{{{{ { }`_{n=0 } ^{$infty$ } }}}} and {v}{{{{ { }`_{n=0 } ^{$infty$ } }}}} are two sequences in D(T) satisfying {{{{ SUM from { { n}=0} to inf }}}}∥un∥<$infty$ and vnlongrightarrow0 as nlongrightarrow$infty$. Suppose that, for any given x0$in$X, the Ishikawa type iteration sequence {xn}{{{{ { }`_{n=0 } ^{$infty$ } }}}} with errors defined by (IS)1 xn+1=(1-${alpha}$n)xn+${alpha}$nSyn+un, yn=(1-${eta}$n)x+${eta}$nSxn+vn for all n=0, 1, 2 … is well-defined. we prove that {xn}{{{{ { }`_{n=0 } ^{$infty$ } }}}} converges strongly to the unique zero of T if and only if {Syn}{{{{ { }`_{n=0 } ^{$infty$ } }}}} is bounded. Several related results deal with iterative approximations of fixed points of ∮-hemicontractions by the ishikawa iteration with errors in a normed linear space. Certain conditions on the iterative parameters {${alpha}$n}{{{{ { }`_{n=0 } ^{$infty$ } }}}} , {${eta}$n}{{{{ { }`_{n=0 } ^{$infty$ } }}}} and t are also given which guarantee the strong convergence of the iteration processes.