Ishikawa Iterative Process for Constructing Solutions of <em>m</em>-Accretive Operator Equations

ZENG Liu-chuan

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(6): 611-618

ZENG Liu-chuan. Ishikawa Iterative Process for Constructing Solutions of m-Accretive Operator Equations[J]. Applied Mathematics and Mechanics, 2002, 23(6): 611-618.

Citation:

ZENG Liu-chuan. Ishikawa Iterative Process for Constructing Solutions of m-Accretive Operator Equations[J]. Applied Mathematics and Mechanics, 2002, 23(6): 611-618.

Citation:

ZENG Liu-chuan. Ishikawa Iterative Process for Constructing Solutions of m-Accretive Operator Equations[J]. Applied Mathematics and Mechanics, 2002, 23(6): 611-618.

PDF( 321 KB)

Ishikawa Iterative Process for Constructing Solutions of m-Accretive Operator Equations

ZENG Liu-chuan

Department of Mathematics, Shanghai Normal University, Shanghai 200234, P R China

Received Date: 2000-07-11
Rev Recd Date: 2001-12-31
Publish Date: 2002-06-15

Abstract

Abstract

The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized.Moreover,the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator equations are established.
- m-accretive operator,
- Ishikawa iterative sequence,
- uniformly smooth Banach space

FullText(HTML)

References(17)

References

[1]	Xu Z B, Roach G F. Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces[J]. J Math Anal Appl,1991,157:189-210.
[2]	Browder F E. Nonlinear mappings of nonexpansive and accretive type in Banach spaces[J]. Bull Amer Math Soc,1967,73:875-882.
[3]	Martin R H, Jr. A global existence theorem for autonomous differential equations in Banach spaces[J]. Proc Amer Math Soc,1970,26:307-314.
[4]	Barbu V. Nonlinear Semigroups and Differential Equations in Banach Spaces[M]. Leyden: Nordhoff,1976.
[5]	Browder F E. Nonlinear monotone and accretive operators in Banach spaces[J]. Proc Nat Acad Sci U S A,1968,61:388-392.
[6]	Liu L S. Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces[J]. J Math Anal Appl,1995,194:114-125.
[7]	Zhu L C. Iterative solution of nonlinear equations involving m-accretive operators in Banach spaces[J]. J Math Anal Appl,1994,188:410-415.
[8]	Chidume C E, Osilike M O. Approximation methods for nonlinear operator equations of the m-accretive type[J]. J Math Anal Appl,1995,189:225-239.
[9]	Liu L S. Ishikawa-type and Mann-type iterative processes with errors for constructing solutions of nonlinear equations involving m-accretive operators in Banach spaces[J]. Nonlinear Anal,1998,34:307-317.
[10]	张石生. m-增生算子方程解的Mann和Ishikawa迭代逼近[J]. 应用数学和力学,1999,20(12):1215-1223.
[11]	Tan K K, Xu H K. Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces[J]. J Math Anal Appl,1993,178:9-21.
[12]	Ding X P. Iterative process with errors of nonlinear equations involving m-accretive operators[J]. J Math Anal Appl,1997,209:191-201.
[13]	Ding X P, Deng L. Iterative solution of nonlinear equations of the monotone and dissipative types in uniformly smooth Banach spaces[J]. J Sichuan Normal Univ,1994,17(1):43-48.
[14]	Zeng L C. Error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth Banach spaces[J]. J Math Anal Appl,1997,209:67-80.
[15]	曾六川. Lipschitz局部强增殖算子的非线性方程的解的迭代构造[J]. 应用数学和力学,16(6):543-552.
[16]	Chang S S, Cho Y J, Lee B S, et al. Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces[J]. J Math Anal Appl,1998,224:149-165.
[17]	Weng X. Fixed point iteration for local strictly pseudo-contractive mappings[J]. Proc Amer Math Soc,1991,113:727-731.