Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces

  • Authors:

  • Yeol Je Cho;Shin Min Kang;Xiaolong Qin

  • Affiliations:

  • Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea;Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea;Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2008

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Abstract

Let C be a closed convex subset of a real uniformly smooth and strictly convex Banach space E. Consider the following iterative algorithm given by {x"0=x@?Carbitrarily chosen ,y"n=@b"nx"n+(1-@b"n)W"nx"n,x"n"+"1=@a"nf(x"n)+(1-@a"n)y"n,@?n=0, where f is a contraction on C and W"n is a mapping generated by an infinite family of nonexpansive mappings {T"i}"i"="1^~. Assume that the set of common fixed points of this infinite family of nonexpansive mappings is not empty. In this paper, we prove that the sequence {x"n} generated by the above iterative algorithm converges strongly to a common fixed point of {T"i}"i"="1^~, which solves some variational inequality. Our results improve and extend the results announced by many others.