The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F（x） = αx （α≥〉 1） for so-called 1-set weakly contractive operators...The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F（x） = αx （α≥〉 1） for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F（x） = αx （α≥1） for such class of operators. As consequences, the main results general- ize and improve the relevant results, which are obtained by O＇Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive （μ-nonexpansive） and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.展开更多
Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also intro...Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for （ws）-compact （in particular nonexpansive） self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.展开更多
We extend the(outer)measureγ_(I) associated to an operator ideal I to a measureγ_(I) for bounded bilinear operators.If I is surjective and closed,and J is the class of those bilinear operators such thatγ_(I)(T)=0,w...We extend the(outer)measureγ_(I) associated to an operator ideal I to a measureγ_(I) for bounded bilinear operators.If I is surjective and closed,and J is the class of those bilinear operators such thatγ_(I)(T)=0,we prove that J coincides with the composition bideal I?B.If I satisfies theΣ_(r)-condition,we establish a simple necessary and sufficient condition for an interpolated operator by the real method to belong to J.Furthermore,if in addition I is symmetric,we prove a formula for the measureγ_(I) of an operator interpolated by the real method.In particular,results apply to weakly compact operators.展开更多
基金Supported in part by the Foundation of Hanshan Normal University, China
文摘The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F（x） = αx （α≥〉 1） for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F（x） = αx （α≥1） for such class of operators. As consequences, the main results general- ize and improve the relevant results, which are obtained by O＇Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive （μ-nonexpansive） and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.
文摘Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for （ws）-compact （in particular nonexpansive） self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.
基金supported in part by UCM(Grant No.PR3/23-30811)。
文摘We extend the(outer)measureγ_(I) associated to an operator ideal I to a measureγ_(I) for bounded bilinear operators.If I is surjective and closed,and J is the class of those bilinear operators such thatγ_(I)(T)=0,we prove that J coincides with the composition bideal I?B.If I satisfies theΣ_(r)-condition,we establish a simple necessary and sufficient condition for an interpolated operator by the real method to belong to J.Furthermore,if in addition I is symmetric,we prove a formula for the measureγ_(I) of an operator interpolated by the real method.In particular,results apply to weakly compact operators.
