Iterative Construction of Solutions to Nonlinear Equations of Strongly Accretive Operators in Banach Spaces
Received:May 28, 1994  
Key Words: strongly accretive   strictly pseudocontractive   p -uniformly smooth Banach space.  
Fund Project:Project supported by the Science and Technology Development Fundation of Shanghai Higher Learning.
Author NameAffiliation
Zeng Luchuan Inst. of Math.
Fudan University
Shanhai 200433
Dept. of Math.
Shanghai Normal University
Shanghai 200234 
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Abstract:
      In this paper, we investigate the Ishikawa iteration process in a p -uniformly smooth Banach space X . Motivated by Deng and Tan and Xu , we prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator from X to X , or to the unique fixed point of T when T is a Lipschitzian and strictly pseudo contractive mapping from a bounded closed convex subset C of X into itself . Our results improve and extend Theorem 4. 1 and 4. 2 of Tan and Xu by removing the restrion in their theorems. These also extend Theorems 1 and 2 of Deng to the p - uniformly smooth Banach space setting.
Citation:
DOI:10.3770/j.issn:1000-341X.1998.03.003
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