An example on the Mann iteration method for Lipschitz pseudocontractions

被引：196

作者：

Chidume, CE ^{[1
]}

Mutangadura, SA

机构：

[1] Abdus Salam Int Ctr Theoret Phys, I-34100 Trieste, Italy

[2] Univ Zimbabwe, Dept Phys, Harare, Zimbabwe

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 08期

关键词：

D O I：

10.1090/S0002-9939-01-06009-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An example of a Lipschitz pseudocontractive map with a unique fixed point is constructed for which the Mann iteration sequence fails to converge. This resolves a long standing open problem.

引用

页码：2359 / 2363

页数：5

共 12 条

[1] FIXED-POINT ITERATIONS FOR REAL FUNCTIONS [J].

BORWEIN, D ;

BORWEIN, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 157 (01) :112-126

[2] NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE [J].

BROWDER, FE .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 54 (04) :1041-&

[3] The Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings [J].

Chang, SS .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1999, 37 (09) :17-24

[4] Global iteration schemes for strongly pseudo-contractive maps [J].

Chidume, CE .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (09) :2641-2649

[5] ZUM PRINZIP DER KONTRAKTIVEN ABBILDUNG [J].

GOHDE, D .

MATHEMATISCHE NACHRICHTEN, 1965, 30 (3-4) :251-&

[6]

HICKS TL, 1979, J MATH ANAL APPL, V59, P498

[7] FIXED-POINTS BY A NEW ITERATION METHOD [J].

ISHIKAWA, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 44 (01) :147-150

[8] A FIXED POINT THEOREM FOR MAPPINGS WHICH DO NOT INCREASE DISTANCES [J].

KIRK, WA .

AMERICAN MATHEMATICAL MONTHLY, 1965, 72 (09) :1004-&

[9]

Krasnoselskii M.A., 1955, Uspekhi Matematicheskikh Nauk, V10, P123, DOI DOI 10.1016/S0076-5392(08)61895-0

[10]

LIU QH, 1990, J MATH ANAL APPL, V148, P55

← 1 2 →