Iterative Construction of Solution to Nonlinear Equations of Lipschitzian and Local Strongly Accretive Operators

Zeng Luchuan

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Zeng Luchuan. Iterative Construction of Solution to Nonlinear Equations of Lipschitzian and Local Strongly Accretive Operators[J]. Applied Mathematics and Mechanics, 1995, 16(6): 543-552.

Citation:

Zeng Luchuan. Iterative Construction of Solution to Nonlinear Equations of Lipschitzian and Local Strongly Accretive Operators[J]. Applied Mathematics and Mechanics, 1995, 16(6): 543-552.

Citation:

Zeng Luchuan. Iterative Construction of Solution to Nonlinear Equations of Lipschitzian and Local Strongly Accretive Operators[J]. Applied Mathematics and Mechanics, 1995, 16(6): 543-552.

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Iterative Construction of Solution to Nonlinear Equations of Lipschitzian and Local Strongly Accretive Operators

Zeng Luchuan

Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

Received Date: 1994-07-04
Publish Date: 1995-06-15

Abstract

Abstract

In this paper,we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X.Let T:X→X be a Lipschitzian and local strongly accretive operator and the set sol(T) of solutions the equation T_x=f be nonempty.We show that soil(T) is a singleton atul the Ishikawa sequence converges strongly to the unique solution of the equation T_x=f.In addition,whenever T is a Lipschitzian and local Psendcontractive mapping from a nonempty convex subset K of X into X and the set F(T) of fixed points of T is nonempty,we prove that F(T) is a singleton and the Ishikawa sequetwe converges strongly to the unique fixed point of T.Our results are the improvements and extension of the results of Deng and Ding^[4] and Tan and Xu^[5].
- local strongly accretive,
- local strictly pseudocontractive,
- puniformly smooth Banach space

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References(8)

References

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