Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (6): 686-693.
曾六川
收稿日期:2000-07-11
修回日期:2001-12-31
出版日期:2002-06-18
发布日期:2002-06-18
基金资助:ZENG Liu-chuan
Received:2000-07-11
Revised:2001-12-31
Online:2002-06-18
Published:2002-06-18
Supported by:摘要: 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.
中图分类号:
曾六川. ISHIKAWA ITERATIVE PROCESS FOR CONSTRUCTING SOLUTIONS OF m-ACCRETIVE OPERATOR EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(6): 686-693.
ZENG Liu-chuan. ISHIKAWA ITERATIVE PROCESS FOR CONSTRUCTING SOLUTIONS OF m-ACCRETIVE OPERATOR EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(6): 686-693.
| [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 types 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 maccretive 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] ZHANG Shi-sheng. Mann and Ishikawa iterative approximation of solutions for m-accretive operator equations[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20 (12):1310-1318. [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] ZENG Liu-chuan. Iterative construction of solutions to nonlinear equations of Lipschitzian and local strongly accretive operators[J]. Applied Mathematics and Mechanics (English Edition), 1995,16(6):583-592. [16] Chang S S, Cho Y J, Lee B S, et al. Iterative approximations of fixed pointsand 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. |
| [1] | Xieping DING, SALAHUDDIN. A system of general nonlinear variational inclusions in Banach spaces[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(12): 1663-1672. |
| [2] | 丁协平. Behavior of solution set for bilevel generalized mixed equilibrium problems in topological vector spaces[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 925-934. |
| [3] | 王方磊;安玉坤. 非线性电报方程组的3个双周期正解问题[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 81-88 . |
| [4] | 张石生;李向荣;陈志坚. 拟变分包含及不动点问题公解的算法[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(5): 571-582 . |
| [5] | 臧小燕;邓磊. Iterative algorithm of solutions for multivalued general mixed implicit equilibrium-like problems[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(4): 477-484 . |
| [6] | 丁协平. Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications (II)[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(12): 1569-1579 . |
| [7] | 张石生;杨莉;柳京爱. Strong convergence theorems for nonexpansive semi-groups in Banach spaces[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(10): 1287-1297 . |
| [8] | 丁协平;林炎诚;姚任文. Three-step relaxed hybrid steepest-descent methods for variational inequalities[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 1029-1036 . |
| [9] | 崔登兰;李养成. Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(2): 229-235 . |
| [10] | 曾六川;姚任之. Sensitivity analysis of generalized set-valued quasi-variational inclusion in Banach spaces[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(1): 97-102 . |
| [11] | 邓磊;杨明歌. Weakly R-KKM mappings---intersection theorems and minimax inequalities in topological spaces[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(1): 103-109 . |
| [12] | 张清邦;丁协平. g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(1): 11-18 . |
| [13] | 丁协平. MAXIMAL ELEMENTS OF A FAMILY OF GB-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(12): 1607-1618 . |
| [14] | . FIXED POINT THEOREMS FOR MAPPINGS SATISFYING IMPLICIT RELATION ON TWO COMPLETE AND COMPACT METRIC SPACES[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(9): 1217-1222 . |
| [15] | 张石生. ON PROBLEM OF NEAREST COMMON FIXED POINT OF NONEXPANSIVE MAPPINGS[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(7): 883-889 . |
| 阅读次数 | ||||||
|
全文 |
|
|||||
|
摘要 |
|
|||||

Email Alert
RSS