In this paper, we investigate the validity of approximation theorm of K. Fan for a demicompact 1-set-contraction map defined on a closed ball,an annulus and a sphere in cones. From this, we improve all recent results ...In this paper, we investigate the validity of approximation theorm of K. Fan for a demicompact 1-set-contraction map defined on a closed ball,an annulus and a sphere in cones. From this, we improve all recent results of Lin [2]. As applications of our theorems, we discuss the existence of positive solutions to twopoint boundary value-problems of differential equations in Banach space. At the same time, the recent main results of (3) established by Guo Dajun are Generalized and supplemented.展开更多
Let E be a uniformly convex Banach space which satisfies Opial’s conditionor has a Frechet differentiable norm.and C be a bounded closed convex subset of E.IfT:C→C is a nonexpansive mapping.then for any initial data...Let E be a uniformly convex Banach space which satisfies Opial’s conditionor has a Frechet differentiable norm.and C be a bounded closed convex subset of E.IfT:C→C is a nonexpansive mapping.then for any initial data x0∈C,the Ishikawaiteration process{xn},defined by xn=tnT(snTxn+(1-sn)xn)+(1-tn)xn,n≥0,converges weakly to a fixed point of T,where{tn}and{sn}are sequences in[0,1]withsome restrictions.展开更多
Let X be a real uniformly smooth Banach space and let T:D(T)(?)X→Xbe (?)-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have...Let X be a real uniformly smooth Banach space and let T:D(T)(?)X→Xbe (?)-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have proved thatthe Mann and Ishikawa iteration processes for T converge strongly to the unique fixedpoint q of T.Several related results deal with iterative solutions of nonlinear equationsinvolving (?)-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach,Zhou and Jia and others.展开更多
文摘In this paper, we investigate the validity of approximation theorm of K. Fan for a demicompact 1-set-contraction map defined on a closed ball,an annulus and a sphere in cones. From this, we improve all recent results of Lin [2]. As applications of our theorems, we discuss the existence of positive solutions to twopoint boundary value-problems of differential equations in Banach space. At the same time, the recent main results of (3) established by Guo Dajun are Generalized and supplemented.
基金Supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,China.
文摘Let E be a uniformly convex Banach space which satisfies Opial’s conditionor has a Frechet differentiable norm.and C be a bounded closed convex subset of E.IfT:C→C is a nonexpansive mapping.then for any initial data x0∈C,the Ishikawaiteration process{xn},defined by xn=tnT(snTxn+(1-sn)xn)+(1-tn)xn,n≥0,converges weakly to a fixed point of T,where{tn}and{sn}are sequences in[0,1]withsome restrictions.
文摘Let X be a real uniformly smooth Banach space and let T:D(T)(?)X→Xbe (?)-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have proved thatthe Mann and Ishikawa iteration processes for T converge strongly to the unique fixedpoint q of T.Several related results deal with iterative solutions of nonlinear equationsinvolving (?)-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach,Zhou and Jia and others.
