• 제목/요약/키워드: Mann iteration

검색결과 48건 처리시간 0.02초

ON THE ON THE CONVERGENCE BETWEEN THE MANN ITERATION AND ISHIKAWA ITERATION FOR THE GENERALIZED LIPSCHITZIAN AND Φ-STRONGLY PSEUDOCONTRACTIVE MAPPINGS

  • Xue, Zhiqun
    • 대한수학회보
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    • 제45권4호
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    • pp.635-644
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    • 2008
  • In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and $\Phi$-strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. 42 (2003), 2645.2651].

CONVERGENCE OF MODIFIED VISCOSITY INEXACT MANN ITERATION FOR A FAMILY OF NONLINEAR MAPPINGS FOR VARIATIONAL INEQUALITY IN CAT(0) SPACES

  • Kyung Soo Kim
    • Nonlinear Functional Analysis and Applications
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    • 제28권4호
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    • pp.1127-1143
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    • 2023
  • The purpose of this paper, we prove convergence theorems of the modified viscosity inexact Mann iteration process for a family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. We also show that the limit of the modified viscosity inexact Mann iteration {xn} solves the solution of some variational inequality.

ITERATION PROCESSES WITH ERRORS FOR NONLINEAR EQUATIONS INVOLVING $\alpha$-STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES

  • Jung, Jong-Soo
    • East Asian mathematical journal
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    • 제17권2호
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    • pp.349-365
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    • 2001
  • Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.

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ISHIKAWA AND MANN ITERATION METHODS FOR STRONGLY ACCRETIVE OPERATORS

  • JONG YEOUL PARK;JAE UG JEONG
    • 대한수학회논문집
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    • 제13권4호
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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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On the Equivalance of Some Fixed Point Iterations

  • Ozdemir, Murat;Akbulut, Sezgin
    • Kyungpook Mathematical Journal
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    • 제46권2호
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    • pp.211-217
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    • 2006
  • In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space.

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COMMON FIXED POINT THEOREMS FOR MANN TYPE ITERATIONS

  • Sharma, Sushil;Deshpande, Bhavana
    • East Asian mathematical journal
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    • 제17권1호
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    • pp.19-32
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    • 2001
  • In this paper, we give some common fixed point theorems for five and six mappings satisfying the Mann-type iteration in Banach spaces. We improve some results of Gornicki and Rhoades, Khan and Imdad, Cho, Fisher and Kang, Cirick and many others.

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ISHIKAWA AND MANN ITERATION METHODS FOR STRONGLY ACCRETIVE OPERATORS

  • JAE UG JEONG
    • Journal of applied mathematics & informatics
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    • 제4권2호
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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 $T_x=f$.

AN EFFICIENT THIRD ORDER MANN-LIKE FIXED POINT SCHEME

  • Pravin, Singh;Virath, Singh;Shivani, Singh
    • Nonlinear Functional Analysis and Applications
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    • 제27권4호
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    • pp.785-795
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    • 2022
  • In this paper, we introduce a Mann-like three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with the other third order iterative methods. Results are presented in a table to support our conclusion.

STRONG CONVERGENCE THEOREMS FOR A QUASI CONTRACTIVE TYPE MAPPING EMPLOYING A NEW ITERATIVE SCHEME WITH AN APPLICATION

  • Chauhan, Surjeet Singh;Utreja, Kiran;Imdad, Mohammad;Ahmadullah, Md
    • 호남수학학술지
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    • 제39권1호
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    • pp.1-25
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    • 2017
  • In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.