Iterative Process to <em>φ</em>-Hemicontractive Operator and <em>φ</em>-Strongly Accretive Operator Equations

DING Xie-ping; ZHANG Hong-lin

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DING Xie-ping, ZHANG Hong-lin. Iterative Process to φ-Hemicontractive Operator and φ-Strongly Accretive Operator Equations[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1133-1139.

Citation:

DING Xie-ping, ZHANG Hong-lin. Iterative Process to φ-Hemicontractive Operator and φ-Strongly Accretive Operator Equations[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1133-1139.

Citation:

DING Xie-ping, ZHANG Hong-lin. Iterative Process to φ-Hemicontractive Operator and φ-Strongly Accretive Operator Equations[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1133-1139.

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Iterative Process to φ-Hemicontractive Operator and φ-Strongly Accretive Operator Equations

Department of Mathematics, Sichuan Normal University, Chengdu 610066, P R China

Received Date: 1999-06-21
Rev Recd Date: 2000-09-20
Publish Date: 2000-11-15

Abstract

Abstract

Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E.Let T:K→K be a uniformly continuous φ-hemicontractive operator with bounded range and {a_n},{b_n},{cn},{a'_n},{b'_n},{c'_n}be sequences in[0,1] satisfying:ⅰ)a_n+b_n+c_n=a'_n+b'_n+c'_n=1,∀n≥0; For any given x0,u0,v0∈K,define the Ishikawa type iterative sequence {x_n} as follows: where {u_n} and {v_n} are bounded sequences in K.Then {x_n} converges strongly to the unique fixed point of T.Related result deals with the convergence of Ishikawa type iterative sequence to the solution of φ-strongly accretive operator equations.
- φ-strongly accretive operator,
- φ-hemicontrictive operator,
- Ishikawa type iterative sequence,
- Banach space

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References(16)

References

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