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
A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set ...A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.展开更多
Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to...Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Taka- hashi by monotone CQ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone CQ method is faster than the hybrid method of Matsushi...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.
基金supported by the National Natural Science Foundation of China (No.11071169)supported by the Research Project of Shaoxing University(No.09LG1002)
文摘A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.
基金the National Natural Science Foundation of China (No.10771050)
文摘Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Taka- hashi by monotone CQ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone CQ method is faster than the hybrid method of Matsushi...
