Ishikawa Iterative Approximations of Solutions to Equations Involving Accretive Operators
Received:March 29, 2002  
Key Words: arbitrary real Banach space   accretive operator   Ishikawa iterative sequence with errors   convergence rate estimate  
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Author NameAffiliation
ZENG Lu-chuan Dept. of Math.
Shanghai Normal University
Shanghai
China 
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Abstract:
      Let X be an arbitrary real Banach space and T : X →X be a Lipschitz continuous accretive operator. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation x+Tx =f. Moreover, our result provides a general convergence rate estimate for the Ishikawa iterative sequence. Utilizing this result, we show that if T : X →X is a Lipschitz continuous strongly accretive operator, then the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation Tx=f.
Citation:
DOI:10.3770/j.issn:1000-341X.2005.01.013
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