Strong convergence theorems for approximating common fixed points of families of nonexpansive mappings and applications

被引：0
作者：
D. R. Sahu
V. Colao
G. Marino
机构：
[1] Banaras Hindu University,Department of Mathematics
[2] Universita della Calabria,Dipartimento di Matematica
来源：
Journal of Global Optimization | 2013年 / 56卷
关键词：
Fixed point; Nonexpansive mappings; Accretive operators; Resolvent operator split feasibility problem; Equilibrium problem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
An implicit algorithm for finding common fixed points of an uncountable family of nonexpansive mappings is proposed. A new inexact iteration method is also proposed for countable family of nonexpansive mappings. Several strong convergence theorems based on our main results are established in the setting of Banach spaces. Both algorithms are applied for finding zeros of accretive operators and for solving convex minimization, split feasibility and equilibrium problems.
引用
收藏
页码：1631 / 1651
页数：20
相关论文
共 94 条
  • [1] Aleyner A.(2005)An explicit construction of sunny nonexpansive retractions in Banach spaces Fixed Point Theory Appl. 3 295-305
  • [2] Reich S.(1977)Variational inequalities, complementarity problems and duality theorems J. Math. Anal. Appl. 58 1-10
  • [3] Allen G.(2007)Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space Nonlinear Anal. 67 2350-2360
  • [4] Aoyama K.(2002)Construction of sunny nonexpansive retractions in Banach spaces Bull. Aust. Math. Soc. 66 9-16
  • [5] Kimura Y.(2003)Iterative solutions for zeros of accretive operators Math. Nachr. 248 62-71
  • [6] Takahashi W.(1996)Generalized monotone bifunctions and equilibrium problems J. Optim. Theory Appl. 90 31-43
  • [7] Toyoda M.(1994)From optimization and variational inequalities to equilibrium problems Math. Stud. 63 123-145
  • [8] Benavides T.D.(1972)Remark on Ky Fans minimax principle Boll. Unione Mat. Ital. 6 293-300
  • [9] Acedo G.L.(1967)Nonlinear mappings of nonexpansive and accetive type in Banach spaces Bull. Am. Math. Soc. 73 875-882
  • [10] Xu H.K.(1973)Properties of fixed-point sets of nonexpansive mappings in Banach spaces Trans. Am. Math. Soc. 179 251-262
12345678910