• 제목/요약/키워드: m-accretive

검색결과 24건 처리시간 0.021초

ON SURJECTIVITY OF m-ACCRETIVE OPERATORS IN BANACH SPACES

  • Han, Song-Ho;Kim, Myeong-Hwan;Park, Jong An.
    • 대한수학회보
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    • 제26권2호
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    • pp.203-209
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    • 1989
  • Recently many authors [2,3,5,6] proved the existence of zeros of accretive operators and estimated the range of m-accretive operators or compact perturbations of m-accretive operators more sharply. Their results could be obtained from differential equations in Banach spaces or iteration methods or Leray-Schauder degree theory. On the other hand Kirk and Schonberg [9] used the domain invariance theorem of Deimling [3] to prove some general minimum principles for continuous accretive operators. Kirk and Schonberg [10] also obtained the range of m-accretive operators (multi-valued and without any continuity assumption) and the implications of an equivalent boundary conditions. Their fundamental tool of proofs is based on a precise analysis of the orbit of resolvents of m-accretive operator at a specified point in its domain. In this paper we obtain a sufficient condition for m-accretive operators to have a zero. From this we derive Theorem 1 of Kirk and Schonberg [10] and some results of Morales [12, 13] and Torrejon[15]. And we further generalize Theorem 5 of Browder [1] by using Theorem 3 of Kirk and Schonberg [10].

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ITERATIVE APPROXIMATION TO M-ACCRETIVE OPERATOR EQUATIONS IN BANACH SPACES

  • Park, Jong An;Park, Yang Seob
    • Korean Journal of Mathematics
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    • 제4권2호
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    • pp.83-88
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    • 1996
  • In 1994 Z.Liang constructed an iterative method for the solution of nonlinear equations involving m-accretive operators in uniformly smooth Banach spaces. In this paper we apply the slight variants of Liang's iterative methods and generalize the results of Z.Liang. Moreover our proof is more simple than Liang's proof.

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Ishikawa-Type And Mann-Type Iterative Processes With Errors For m-Accretive Operators

  • Park, Jong-Yeoul;Jeong, Jae-Ug
    • 대한수학회논문집
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    • 제15권2호
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    • pp.309-323
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    • 2000
  • The purposes of this paper are to revise the definitions of Ishikawa and Mann type iterative processes with errors, to study the unique solution of the m-accretive operator equation x+Tx=f and the convergence problem of Ishikawa and Mann type iterative processes with errors for m-accretive mappings without the Lipschitz condition. The results presented in this paper improve, extend, and unify the corresponding results in [4, 7, 8, 12, 16] in more general setting.

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ITERATIVE SOLUTIONS TO NONLINEAR EQUATIONS OF THE ACCRETIVE TYPE IN BANACH SPACES

  • Liu, Zeqing;Zhang, Lili;Kang, Shin-Min
    • East Asian mathematical journal
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    • 제17권2호
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    • pp.265-273
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    • 2001
  • In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

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ITERATIVE SOLUTION OF NONLINEAR EQUATIONS WITH STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES

  • Jeong, Jae-Ug
    • Journal of applied mathematics & informatics
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    • 제7권2호
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    • pp.605-615
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    • 2000
  • Let E be a real Banach space with property (U,${\lambda}$,m+1,m);${\lambda}{\ge}$0; m${\in}N$, and let C be a nonempty closed convex and bounded subset of E. Suppose T: $C{\leftrightarro}C$ is a strongly accretive map, It is proved that each of the two well known fixed point iteration methods( the Mann and Ishikawa iteration methods.), under suitable conditions , converges strongly to a solution of the equation Tx=f.

ITERATIVE PROCESS WITH ERRORS FOR m-ACCRETIVE OPERATORS

  • Baek, J.H;Cho, Y.J.;Chang, S.S
    • 대한수학회지
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    • 제35권1호
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    • pp.191-205
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    • 1998
  • In this paper, we prove that the Mann and Ishikawa iteration sequences with errors converge strongly to the unique solution of the equation x + Tx = f, where T is an m-accretive operator in uniformly smooth Banach spaces. Our results extend and improve those of Chidume, Ding, Zhu and others.

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GENERAL NONLINEAR RANDOM SET-VALUED VARIATIONAL INCLUSION PROBLEMS WITH RANDOM FUZZY MAPPINGS IN BANACH SPACES

  • Balooee, Javad
    • 대한수학회논문집
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    • 제28권2호
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    • pp.243-267
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    • 2013
  • This paper is dedicated to study a new class of general nonlinear random A-maximal $m$-relaxed ${\eta}$-accretive (so called (A, ${\eta}$)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in $q$-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal $m$-relaxed ${\eta}$-accretive mappings due to Lan et al. and Chang's lemma [13], some new iterative algorithms with mixed errors for finding the approximate solutions of the aforesaid class of nonlinear random equations are constructed. The convergence analysis of the proposed iterative algorithms under some suitable conditions are also studied.

ASYMPTOTIC BEHAVIOR OF GENERALIZED SOLUTIONS IN BANACH SPACES

  • Lee, Gu-Dae;Park, Jong-Yeoul
    • 대한수학회보
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    • 제23권2호
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    • pp.123-132
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    • 1986
  • Let X be a real Banach space with norm vertical bar . vertical bar and let I denote the identity operator. Then an operator A.contnd.X*X with domain D(A) and range R(A) is said to be accretive if vertical bar x$_{1}$-x$_{2}$ vertical bar.leq.vertical bar x$_{1}$-x$_{2}$+r(y$_{1}$-y$_{2}$) vertical bar for all y$_{i}$.mem.Ax$_{i}$, i=1, 2, and r>0. An accretive operator A.contnd.X*X is m-accretive if R(I+rA)=X for all r>0.r>0.

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ITERATIVE ALGORITHMS WITH ERRORS FOR ZEROS OF ACCRETIVE OPERATORS IN BANACH SPACES

  • Jung, Jong-Soo
    • Journal of applied mathematics & informatics
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    • 제20권1_2호
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    • pp.369-389
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    • 2006
  • The iterative algorithms with errors for solutions to accretive operator inclusions are investigated in Banach spaces, including a modification of Rockafellar's proximal point algorithm. Some applications are given in Hilbert spaces. Our results improve the corresponding results in [1, 15-17, 29, 35].

NOOR ITERATIONS FOR NONLINEAR LIPSCHITZIAN STRONGLY ACCRETIVE MAPPINGS

  • Jeong, Jae-Ug;Noor, M.-Aslam;Rafig, A.
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제11권4호
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    • pp.337-348
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    • 2004
  • In this paper, we suggest and analyze Noor (three-step) iterative scheme for solving nonlinear strongly accretive operator equation Tχ = f. The results obtained in this paper represent an extension as well as refinement of previous known results.

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