Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K ...Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.展开更多
In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak （k, k＇） contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T1 ： Xγ...In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak （k, k＇） contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T1 ： XγY→ X and T2 ： XγY → Y be two operators which satisfy weak （k, k＇） contractive type condition. Using T1 and T2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γY. We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings （T1, T2） satisfying weak （k, k＇） contractive type condition on X γ Y and from this pair, we also obtain two self mappings S1 and S2 on X and Y respectively with unique fixed points.展开更多
In this paper,we prove fixed point theorem for weakly contractive mappings using locally T-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general ...In this paper,we prove fixed point theorem for weakly contractive mappings using locally T-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions.Our fixed point results under universal relation reduces to Harjani and Sadarangani[Nonlinear Anal.,71(2009),3403-3410]fixed point theorems.In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.展开更多
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 none...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.展开更多
文摘Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.
文摘In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak （k, k＇） contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T1 ： XγY→ X and T2 ： XγY → Y be two operators which satisfy weak （k, k＇） contractive type condition. Using T1 and T2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γY. We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings （T1, T2） satisfying weak （k, k＇） contractive type condition on X γ Y and from this pair, we also obtain two self mappings S1 and S2 on X and Y respectively with unique fixed points.
文摘In this paper,we prove fixed point theorem for weakly contractive mappings using locally T-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions.Our fixed point results under universal relation reduces to Harjani and Sadarangani[Nonlinear Anal.,71(2009),3403-3410]fixed point theorems.In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.
基金supported by the Natural Science Foundation of Yibin University(No.2009Z3)
文摘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.
