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.
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页数：9
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