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1.
ITERATIVE APPROXIMATION WITH ERRORS OF FIXED POINT FOR A CLASS OF NONLINEAR OPERATOR WITH A BOUNDED RANGE 总被引:2,自引:0,他引:2
1IntroductionandPreliminariesLetXbearealBanachspacewithnorm||·||andadualX*.ThenormalizeddualitymappingJ:X→2Xisdefinedbywhere<·,·>denotesthegeneralizeddualitypairing.Itiswell-knownthatifX*isstrictlyconvex,thenJissingle-valuedandsuchthatJ(tx)=tJxforallt≥0,x∈X.IfX*isunifomilyconvex,thenJisuniformlycontinuousonanyboundedsubsetsofX(of.Browder[1]andBarbu[2])OperatorTwithdomainD(T)andrangeR(T)inXissaidtobeaccretiveifforeveryx,y6D(T),thereexistsajeJ(x--y)suchthatTheconceptofaccretive… 相似文献
2.
Iterative solution of nonlinear equations with strongly accretive operators in Banach spaces 总被引:1,自引:0,他引:1
周海云 《应用数学和力学(英文版)》1999,20(3):282-289
1IntroductionandPreliminariesLetXbearealBanachspacewithnormIJ'11andadualX'.ThenormalizeddualitymappingJ:X~ZxisdefinedbyJx={x'eX*I(x,x')=11x112=11x if'},where',')denotesthegeneralizeddualitypairing.Itiswell-knownthatifX isstrictlyconvex,Jissingle-valuedandJ(tx)=tjxforallt201xeX.IfX*isuniformlyconvex,thenJisuniformlycontinuousonanyboundedsubsetSofX(of.Browde,fljandBarbuL2]).AnoperatorTwithdomainD(T)andrangeR(T)inXissaidtobeaccretiveifforeveryx,y6D(T),thereexistsajeJ(x--y)suchthat(T… 相似文献
3.
REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES 总被引:2,自引:0,他引:2
1 IntroductionandPreliminariesSupposeEisarealBanachspaceandTisaselfmapofE .Supposex0 ∈Eandxn+1=f(T ,xn)definesaniterationprocedurewhichyieldsasequenceofpoints xn ∞n=0 inE .Foranexample ,thefunctioniterationxn+1=f(T ,xn) =Tx0 .SupposeF(T) =x∈E :Tx=x ≠ andthat xn convergess… 相似文献
4.
A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces. 相似文献
5.
Proximal point algorithm with errors for generalized strongly nonlinear quasivariational inclusions 总被引:1,自引:0,他引:1
丁协平 《应用数学和力学(英文版)》1998,19(7):637-643
I.IntroductionLetHbeaHibertspaceendowedwithanorm11'11andaninnerproduct',.)andC(H)bethefamilyofallnonemptycompactsubsetsofH.LetT,A:H~C(H)besetvaluedmappings,g:H~Hbeasingle-valuedmappingand9:HxH~RU{ ac}besuchthatforeachfixedyeH,9.,y):H~RUt co}isaproperconvexlowersemicontinuousfunctiononHandg(H)ndomag'Y)#oforeachyeH,ThentheproblemoffindingxeH,ueT(x)andveA(x)suchthatg(x)edomag',x)and(u~v,y~g(x))39(g(x)'x)~9(y'x)(VYeH)(l.l)iscalledthegeneralizedstronglynonlinearquasivariationalinclusio… 相似文献
6.
Zeng Liu-chuan 《应用数学和力学(英文版)》2002,23(6):686-693
The convergence of theIshikawa 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.
Foundation items: the National Natural Science Foundation of China (19801023); the Teaching and Research Award Fund for Outstanding Young
Teachers in Higher Education Institutions of MOE, China
Biography: ZENG Liu-chuan (1965-), Professor 相似文献
7.
陈远汉 《应用数学和力学(英文版)》1984,5(1):1121-1135
In the present paper, a finite element mixed variational functional and the iterative equations of the eccentric orthogonal stiffened plates are developed in accordance with nonlinear elasticity. By using an important technique the coupling coefficients of the two-dimensional coupling matrix are resolved into the known input data in the programming which is a three-dimensional coefficient matrix. The nonlinear equations are transformed into the instantaneous linear equations; and by using the conjugate gradient method the linear equations are solved. As a result, therefore, the calculation is enormously simplified, the precision manifested, and a satisfactory result obtained. 相似文献
8.
Iterative construction of solutions to nonlinear equations of lipschitzian and local strongly accretive operators 总被引:2,自引:0,他引:2
曾六川 《应用数学和力学(英文版)》1995,16(6):583-592
In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. Let T: X→X be a Lipschitzian
and local strongly accretive operator and the set sol(T) of solutions of the equation Tx=f be nonempty. We show that sol(T)
is a singleton and the Ishikawa sequence converges strongly to the unique solution of the equation Tx=f. In addition, whenever
T is a Lipschitzian and local pseudocontractive mapping from a nonempty convex subset K of X and the set F(T) of fixed points
of T is nonempty, we prove that F(T) is a singleton and the Ishikawa sequence converges strongly to the unique fixed point
of T. Our results are the improvements and extension of the results of Deng and Ding(4) and Tan and Xu(5). 相似文献
9.
何穷 《应用数学和力学(英文版)》1982,3(2):293-302
In this paper, the force method of statically indeterminate structure mechanics is used to treat the solids of revolution with discrete fixed supports. The reactionary forces of discrete fixed supports are considered as statically indeterminate unknown variables. The force-method canonical equations, in which the coefficient matrix and the right-hand vector are computed by semi-analytical finite element method, are solved. Then the finite element solution of solid of revolution with discrete fixed supports is calculated with the external loads superposed from the assigned external loads and the reactionary forces of discrete supports. 相似文献
10.
Existence and Approximation of Solutions to Variational Inclusions with Accretive Mappings in Banach Spaces 总被引:3,自引:0,他引:3
张石生 《应用数学和力学(英文版)》2001,22(9):997-1003
IntroductionThroughoutthispaperwesupposethatXisarealBanachspace,X isitsdualspace ,〈· ,·〉isthepairingofXandX .D(T)andR(T)denotethedomainandtherangeofTrespectively .LetT ,A :X →X ,g :X→X bethreemappingsandφ :X →R∪ ∞ aproperconvexlowersemi_continuousfunction .In 1 999,th… 相似文献
11.
Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi- contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L . B . Ciric , Q . H. Liu , H. E. Rhoades and H. K. Xu , et al. , but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces . 相似文献
12.
This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.(Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715(2009)),Plubtieng and Punpaeng(Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469(2007)),Colao et al.(Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352(2008)),Yao et al.(Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363(2007)DOI 10.1155/2007/64363),and others. 相似文献
13.
SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONSShiYuaning(史玉明)... 相似文献
14.
Blowup properties for a class of nonlinear degenerate diffusion equation with nonlocal source 总被引:2,自引:0,他引:2
A nonlinear degenerate parabolic equation with nonlocal source was considered. It was shown that under certain assumptions the solution of the equation blows up in finite time and the set of blowup points is the whole region. The integral method is used to investigate the blowup properties of the solution. 相似文献
15.
A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem is constructed. 相似文献
16.
V. I. Slyn’ko 《International Applied Mechanics》2008,44(7):818-829
The mechanisms whereby a double pendulum with vibrating point of suspension loses stability in equilibrium positions are studied.
Stability conditions for the equilibrium positions in critical cases are established
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 120–133, July 2008. 相似文献
17.
SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES 总被引:3,自引:0,他引:3
IntroductionAninterestingfeatureinthefreevibrationofanonlinearsystemisthefactthatthenumberofexistingnormalmodesmayexceedthenumberofdegreesoffreedom ,aphenomenonnotencounteredinalinearsystemandcausedbymodebifurcation .Thereforemuchworkhasbeendoneonthest… 相似文献
18.
The paper addresses a problem of plane elasticity for a doubly connected body with outer and inner boundaries in the form
of regular polygons with a common center and parallel sides. The neighborhoods of the vertices of the inner boundary are unknown
equal full-strength smooth arcs symmetric about the rays coming from the vertices to the center. It is assumed that this elastic
body is inserted into a hole of a rigid body, with the hole boundary coinciding with the outer boundary of the elastic body.
Absolutely smooth rigid punches with rectilinear bases are pressed into all the rectilinear sections of the inner polygonal
boundary of the elastic body. There is no friction between the elastic and rigid bodies. The unknown arcs are free from external
stresses. Complex variable theory is used to determine the unknown arcs and the stress state of the elastic body
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 110–118, March 2006. 相似文献