Zhou Haiyun. Iterative Solution of Nonlinear Equations with Strongly Accretive Operators in Banach Spaces[J]. Applied Mathematics and Mechanics, 1999, 20(3): 269-276.
Citation: Zhou Haiyun. Iterative Solution of Nonlinear Equations with Strongly Accretive Operators in Banach Spaces[J]. Applied Mathematics and Mechanics, 1999, 20(3): 269-276.

Iterative Solution of Nonlinear Equations with Strongly Accretive Operators in Banach Spaces

  • Received Date: 1997-04-28
  • Rev Recd Date: 1998-04-05
  • Publish Date: 1999-03-15
  • :Let X be a real Banach space with a uniformly convex dual X*. Let T :X y X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L≥1 and a strongly accretive constant k∈(0,1). Let {αn},{βn}. be two real sequence in [0,1] satisfying:(ⅰ)αn→0(n→∞);(ⅱ)βn<L(1+L)/k(1-k)(n≥0);(ⅲ) Set Sx=f-Tx+x Assume that be two sequences in X satisfying =o(βn)与μn→0(n→∞).For arbitrary x0X the iteration sequence {xn} is defined by IS)1xn+1=(1-αn)xnnSyn+unyn=(1-βn)xnnSxnn(n≥0) then {xn converges strongly to the unique solution of the equation Tx=f A related result deals with iterative approximation of fixed points of φhemicontractive mappings.
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