Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (12): 1310-1318.
• Articles • Previous Articles Next Articles
Zhang Shisheng
Received:1998-03-27
Revised:1999-05-31
Online:1999-12-18
Published:1999-12-18
Supported by:2010 MSC Number:
Zhang Shisheng . MANN AND ISHIKAWA ITERATIVE APPROXIMATION OF SOLUTIONS FOR m-ACCRETIVE OPERATOR EQUATIONS. Applied Mathematics and Mechanics (English Edition), 1999, 20(12): 1310-1318.
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| [1] Lindehstrauss J, Tsafriri L. Classical Banach Spaces Ⅱ[M]. New York/Berlin:Springer-Verlag ,1979.
[2] Xu Z B, Roach G F. Characteristic inequalities of uniformly convex and uniformlysmooth Banach spaces[J]. JMath Anal Appl,1991,157:189~210. [3] Browder FE,Nonlinear mappings of nonexpansive and accretivetypein Banach spaces[J]. Bull Amer Math Soc,1967 ,73 :875~882. [4] Kato T.Nonlinearsemigroupsand evolution equations[J].JMath SocJapan,1967,19:508~520. [5] Martin RH,Jr.Aglobalexistencetheorem forautonomous differentialequationsin Ba nach spaces[J]. Proc Amer Math Soc,1970,26:307~314. [6] Ishikawa S.Fixed points by a new iterative method[J]. Proc Amer Math Soc,1974,44:147~150. [7] Mann W R. Mean value method in iteration[J]. Proc Amer Math Soc,1953 ,4:506~510. [8] Chidume CE.An approximation method for monotone Lipschitzian operatorsin Hilbertspace[J]. JAustral Math Soc,1986,41:59~63. [9] Chidume CE.Iterative solution of nonlinear equations ofthe monotone and dissipativetypes[J]. Appl Anal,1989,33:79~86. [10] Chidume CE.Iterative solution of nonlinear equations ofthe monotone type in Banachspaces[J]. Bull Austral Math Soc,1990,42:21~31. [11] Deng Lei,Ding Xieping .Iterative processfor Lipschitzlocalstricitly pseudo-contractivemappings[J].Applied Mathematics and Mechanics ( English Ed),1994 ,15(2):119~123 . [12] Deng Lei,Ding Xieping.Iterative approximation of Lipschitz strictly pseudo-contractivemappingsin uniformly smooth Banach space[J]. Nonlinear Appl,1995 ,24 :981~987. [13] Ding Xieping, Deng Lei.Iterative solution of nonlinear equations ofthe monotone anddissipativetypesin uniformly smooth Banach spaces[J]. JSichuan Normal Univ,1994,17(1) :43~48.(in Chinese) [14] Tan KK,Xu HK.Iterative solutionsto nonlinearequations ofstrongly accretive opera torsin Banach spaces[J]. JMath Anal Appl,1993,178:9~21. [15] Chang SS,Cho YJ,Lee BS,etal.Iterative approximationsoffixed pointsandsolu-tionsfor strongly accretive and strongly pseudo-contractive mappings in Banach spaces[J].JMath Anal Appl,1998 ,224:149~165. [16] Chidume CE.Iterativeapproximation offixed points of Lipschitzian strictly pseudo-con tractive mappings[J]. Proc Amer Math Soc,1987 ,99 :283~288. [17] Chidume CE.Aniterative processfornonlinear Lipschitzian strongly accretive mappingsin Lpspaces[J].JMath Anal Appl,1990 ,151:453~461 . [18] Chidume CE. Approximation offixed points of strongly pseudo-contractive mappings[J]. Proc Amer Math Soc,1994 ,120:545~551 . [19] Zhu LC.Iterativesolution ofnonlinearequationsinvolving m -accretive operatorsin Ba nach spaces[J].JMath Anal Appl,1994 ,188:410~415. [20] Chidume CE,Osilike M O.Approximation methodsfor nonlinear operatorequations ofthe m-accretivetype[J].JMath Anal Appl,1995 ,189:225~239 . [21] Chang SS,Tan KK.Iteration processesforapproximation fixed points of operators ofmonotonetype[J]. Bull Austral Math Soc,1998 ,57:433~445. [22] Liu LS.Ishikawa and Manniterative process with errorsfornonlinearstrongly accretivemappingsin Banachspaces[J].JMath Anal Appl,1995,194:114~125. [23] Bruck RE.Theiterativesolution oftheequation y ∈x + Txfora monotone operator Tin Hilbertspace[J]. Bull Amer Math Soc,1973 ,79:1258~1262. [24] Chang SS.Some problemsandresultsinthetheory ofnonlinearanalysis[J]. NonlinearAnalysis TMA,1997 ,30(7) :4197~4208 . [25] Ding Xieping.Iterative process with errors of nonlinear equationsinvolving m-accretiveoperators[J]. JMath Anal Appl,1997,209 :191~201 . [26] Zeng Luchuan.Errorboundsforapproximationsolutionsto nonlinearequationsofstrong ly accretive operatorsin uniformly smooth Banach spaces[J]. JMath Anal Appl,1997,209:67~80. [27] Barbu V. Nonlinear Semigroups and DifferentialEquationsin Banach Spaces[M].Ley den:Noordhoff,1976. [28] Browder FE.Nonlinear monotone and accretive operatorsin Banach spaces[J]. ProcNat Acad Sci USA,1968,61 :388~392. [29] Nevanlinna O.Reich S.Strong convergence ofcontraction semi-groups and ofiterativemethodsforaccretive operatorsin Banach spaces[J].IsraelJMath,1979,32:44~58. [30] Osilike MO.Approximation methodsfornonlinear m-accretive operatorequations[J].JMath Anal Appl,1997 ,209:20~24. [31] Reich S.An iterative procedureforconstructing zeros ofaccretive setsin Banach spaces[J]. Nonlinear Anal,1978,2 :85~92 . [32] Reich S.Strongly convergence theorems forresolvents ofaccretive operatorsin Banachspaces[J].JMath Anal Appl,1980 ,75 :287~292. [33] Weng X.Fixed pointiteration forlocalstrictly pseudo-contractive mappings[J]. ProcAmer Math Soc,1991,113:727~731 . [34] Zeng Liuchuan.Iterative construction of solutionsto nonlinear equations of Lipschitzianandlocalstrongly accretive operators[J].Applied Mathematics and Mechanics (English Ed),1995 ,16(6):583~592. |
| [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] | Xie-ping DING . 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] | Fang-lei WANG;Yu-kun AN . Three positive doubly periodic solutions of a nonlinear telegraph system [J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 81-88 . |
| [4] | ZHANG Shi-sheng;LEE Joseph H. W.;CHAN Chi Kin. Algorithms of common solutions to quasi variational inclusion and fixed point problems [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(5): 571-582 . |
| [5] | ZANG Xiao-yan;DENG Lei. 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] | DING Xie-ping. null [J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(12): 1569-1579 . |
| [7] | ZHANG Shi-sheng;YANG Li;LIU Jing-ai. Strong convergence theorems for nonexpansive semi-groups in Banach spaces [J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(10): 1287-1297 . |
| [8] | DING Xie-ping;LIN Yen-cherng;YAO Jen-chih. Three-step relaxed hybrid steepest-descent methods for variational inequalities [J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 1029-1036 . |
| [9] | CUI Deng-lan;LI Yang-cheng. 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] |
ZENG Lu-chuan;YAO Jen-chih.
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] | DENG Lei;YANG Ming-ge. 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] | ZHANG Qing-bang;DING Xie-ping. 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] | DING Xie-ping. 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] | Abdlkrim Aliouche;Brian Fisher. 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] | ZHANG Shi-sheng. ON PROBLEM OF NEAREST COMMON FIXED POINT OF NONEXPANSIVE MAPPINGS [J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(7): 883-889 . |
| Viewed | ||||||
|
Full text |
|
|||||
|
Abstract |
|
|||||

Email Alert
RSS