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

Zhou Haiyun

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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.

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.

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

Zhou Haiyun

Department of Basic Science, Ordnance Engineering College, Shijiazhuang 050003, P. R. China

Received Date: 1997-04-28
Rev Recd Date: 1998-04-05
Publish Date: 1999-03-15

Abstract

Abstract

: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 {α_n},{β_n}. be two real sequence in [0,1] satisfying:(ⅰ)α_n→0(n→∞);(ⅱ)β_n<L(1+L)/k(1-k)(n≥0);(ⅲ) Set Sx=f-Tx+x Assume that be two sequences in X satisfying =o(β_n)与μ_n→0(n→∞).For arbitrary x₀∈X the iteration sequence {x_n} is defined by IS)1x_n+1=(1-α_n)x_n+α_nSy_n+u_ny_n=(1-β_n)x_n+β_nSx_n+μ_n(_n≥0) then {x_n converges strongly to the unique solution of the equation Tx=f A related result deals with iterative approximation of fixed points of φhemicontractive mappings.
- Ishikawa iteration with errors,
- strongly accretive mapping,
- φ-hemicontractive mapping

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References(32)

References

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