• Title/Summary/Keyword: Accretive operators

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ALMOST STABILITY OF ISHIKAWA ITERATIVE SCHEMES WITH ERRORS FOR φ-STRONGLY QUASI-ACCRETIVE AND φ-HEMICONTRACTIVE OPERATORS

  • Kim, Jong-Kyu;Liu, Ze-Qing;Kang, Shin-Min
    • Communications of the Korean Mathematical Society
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    • v.19 no.2
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    • pp.267-281
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    • 2004
  • In this paper, we establish almost stability of Ishikawa iterative schemes with errors for the classes of Lipschitz $\phi$-strongly quasi-accretive operators and Lipschitz $\phi$-hemicontractive operators in arbitrary Banach spaces. The results of this paper extend a few well-known recent results.

A SYSTEM OF VARIATIONAL INCLUSIONS IN BANACH SPACES

  • Liu, Zeqing;Zhao, Liangshi;Hwang, Hong-Taek;Kang, Shin-Min
    • East Asian mathematical journal
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    • v.26 no.5
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    • pp.681-691
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    • 2010
  • A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

VISCOSITY METHODS OF APPROXIMATION FOR A COMMON SOLUTION OF A FINITE FAMILY OF ACCRETIVE OPERATORS

  • Chen, Jun-Min;Zhang, Li-Juan;Fan, Tie-Gang
    • East Asian mathematical journal
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    • v.27 no.1
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    • pp.11-21
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    • 2011
  • In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

ISHIKAWA AND MANN ITERATION METHODS FOR STRONGLY ACCRETIVE OPERATORS

  • JAE UG JEONG
    • Journal of applied mathematics & informatics
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    • v.4 no.2
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    • pp.477-485
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    • 1997
  • Let E be a smooth Banach space. Suppose T:$E \rightarrow E$ 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 $T_x=f$.

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

  • Jung, Jong-Soo
    • Journal of applied mathematics & informatics
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    • v.20 no.1_2
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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].

ISHIKAWA AND MANN ITERATION METHODS FOR STRONGLY ACCRETIVE OPERATORS

  • JONG YEOUL PARK;JAE UG JEONG
    • Communications of the Korean Mathematical Society
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    • v.13 no.4
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    • pp.765-773
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    • 1998
  • Let E be a smooth Banach space. Suppose T : E longrightarrow E 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.

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ITERATIVE PROCESS WITH ERRORS FOR m-ACCRETIVE OPERATORS

  • Baek, J.H;Cho, Y.J.;Chang, S.S
    • Journal of the Korean Mathematical Society
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    • v.35 no.1
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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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STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR FINDING COMMON ZEROS OF A FINITE FAMILY OF ACCRETIVE OPERATORS

  • Jung, Jong-Soo
    • Communications of the Korean Mathematical Society
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    • v.24 no.3
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    • pp.381-393
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    • 2009
  • Strong convergence theorems on viscosity approximation methods for finding a common zero of a finite family accretive operators are established in a reflexive and strictly Banach space having a uniformly G$\hat{a}$teaux differentiable norm. The main theorems supplement the recent corresponding results of Wong et al. [29] and Zegeye and Shahzad [32] to the viscosity method together with different control conditions. Our results also improve the corresponding results of [9, 16, 18, 19, 25] for finite nonexpansive mappings to the case of finite pseudocontractive mappings.