ISHIKAWA ITERATION PROCESS FOR NONLINEAR LIPSCHITZ STRONGLY ACCRETIVE MAPPINGS

被引：54
作者：
CHIDUME, CE [1 ]
OSILIKE, MO [1 ]
机构：
[1] UNIV NIGERIA,DEPT MATH,NSUKKA,NIGERIA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1995年 / 192卷 / 03期
关键词：
D O I：
10.1006/jmaa.1995.1200
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let E = L(p), p greater than or equal to 2 and let T:E --> E be a Lipschitzian and strongly accretive mapping. Let S:E --> E be defined by Sx = f - Tx + x. It is proved that under suitable conditions on the real sequences {alpha(n)}(infinity)(n=0) and {beta(n)}(infinity)(n=0), the iteration process, x(0) is an element of E, x(n+1) = (1 - alpha(n))x(n) + alpha(n)S[(1 - beta(n))x(n) + beta(n)Sx(n)], n greater than or equal to 0, converges strongly to the unique solution of Tx = f. A related result deals with the iterative approximation of fixed points for Lipschitz strongly pseudocontractive mappings in E. A consequence of our result gives an affirmative answer to a problem posed by C. E. Chidume (J. Math. Anal. Appl. 151, No. 2 (1990), 453-461). (C) 1995 Academic Press, Inc.
引用
收藏
页码：727 / 741
页数：15
相关论文
共 36 条
[1]  
Bogin J., On Strict Pseudocontractions and a Fixed Point Theorem, (1974)
[2]  
Borwein J., Reich S., Shafrir I., Krasnoseski-Mann iterations in normed spaces, Canad. Math. Bull, 35, pp. 21-28, (1992)
[3]  
Browder F.E., Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc, 73, pp. 875-882, (1967)
[4]  
Browder F.E., Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math, (1976)
[5]  
Browder F.E., Petryshyn W.V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl, 20, pp. 197-228, (1967)
[6]  
Bynum W.L., Weak parallelogram laws for Banach spaces, Canad. Math. Bull, 19, 3, pp. 269-275, (1976)
[7]  
Bruck R.E., The iterative solution of the equation/e x + Tx for a monotone operator T in Hilbert space, Bull. Amer. Math. Soc, 79, pp. 1258-1262, (1973)
[8]  
Chidume C.E., Iterative approximation of fixed points of Lipschitzian strictly pseudo-contractive mappings, Proc. Amer. Math. Soc, 99, 2, pp. 283-288, (1987)
[9]  
Chidume C.E., Iterative solution of nonlinear equations of the monotone and dissipative types, Appl. Anal, 33, pp. 79-86, (1989)
[10]  
Chidume C.E., An approximation method for monotone Lipschitzian operators in Hilbert spaces, J. Austral. Math. Soc. Ser. A, 41, pp. 59-63, (1986)
1234