The implicit midpoint rule for nonexpansive mappings

被引：43

作者：

Alghamdi, Maryam A. ^{[1
]}

Alghamdi, Mohammad Ali ^{[2
]}

Shahzad, Naseer ^{[2
]}

Xu, Hong-Kun ^{[2
,3
]}

机构：

[1] King Abdulaziz Univ, Sci Fac Girls, Dept Math, Jeddah 21491, Saudi Arabia

[2] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

[3] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

来源：

FIXED POINT THEORY AND APPLICATIONS | 2014年

关键词：

implicit midpoint rule; nonexpansive mapping; periodic solution; nonlinear evolution equation; Fredholm integral equation; Hilbert space; ORDINARY DIFFERENTIAL-EQUATIONS; BOUNDARY-VALUE-PROBLEMS; FIXED-POINTS; SPACES; APPROXIMATION; EXTRAPOLATION; ITERATION;

D O I：

10.1186/1687-1812-2014-96

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The implicit midpoint rule (IMR) for nonexpansive mappings is established. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a Hilbert space. Applications to the periodic solution of a nonlinear time-dependent evolution equation and to a Fredholm integral equation are included.

引用

页数：9

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