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Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings 被引量:1
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作者 WANG Ya-qin 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第10期1691-1694,共4页
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
关键词 Viscosity approximation methods weakly contractive mapping Fixed point weakly sequentially continuous duality mapping
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Viscosity approximation with weak contractions for fixed point problem,equilibrium problem,and variational inequality problem
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作者 张石生 李向荣 +1 位作者 陈志坚 柳京爱 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第10期1273-1282,共10页
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
关键词 viscosity approximation weak contraction mapping equilibrium problem nonexpansive mapping implicit iteration minimization problem
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Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application
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作者 Gopi Prasad Ramesh Chandra Dimri 《Analysis in Theory and Applications》 CSCD 2022年第2期232-242,共11页
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
关键词 R-continuity locally T-transitive binary relation weakly contractive map
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