대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제25권4호
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  • Pages.583-607
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  • 2010
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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CONVERGENCE THEOREMS FOR TWO FAMILIES OF WEAK RELATIVELY NONEXPANSIVE MAPPINGS AND A FAMILY OF EQUILIBRIUM PROBLEMS

  • Zhang, Xin (DEPARTMENT OF MATHEMATICS TIANJIN POLYTECHNIC UNIVERSITY) ;
  • Su, Yongfu (DEPARTMENT OF MATHEMATICS TIANJIN POLYTECHNIC UNIVERSITY)
  • 투고 : 2009.11.11
  • 발행 : 2010.10.31
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초록

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616?5628] and some other papers.

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참고문헌

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피인용 문헌

  1. Strong Convergence of Modified Iteration Processes for Relatively Weak Nonexpansive Mappings vol.52, pp.4, 2012, https://doi.org/10.5666/KMJ.2012.52.4.433