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STRONG CONVERGENCE OF HYBRID ITERATIVE SCHEMES WITH ERRORS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS

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In this paper, we prove a strong convergence result under an iterative scheme for N nite asymptotically ki-strictly pseudo-contractive mappings and a rmly nonexpansive mappings Sr. Then, we modify this algorithm to obtain a strong convergence result by hybrid methods. Our results extend and unify the cor- responding ones in [1, 2, 3, 8]. In particular, some necessary and sufficient conditions for strong convergence under Algorithm 1.1 are obtained.

Abstract

In this paper, we prove a strong convergence result under an iterative scheme for N nite asymptotically ki-strictly pseudo-contractive mappings and a rmly nonexpansive mappings Sr. Then, we modify this algorithm to obtain a strong convergence result by hybrid methods. Our results extend and unify the cor- responding ones in [1, 2, 3, 8]. In particular, some necessary and sufficient conditions for strong convergence under Algorithm 1.1 are obtained.

참고문헌 (8)

  1. L.C. Ceng, "An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings", J. Comp. Appl. Math., 223, pp.967~974 (2009)[DOI]
  2. S.H. Kim, "Two-steps hybrid iterative scheme with errors for generalized equilibrium problems and common fixed point problems", Appl. Math. ENotes, 15, pp.276~286 (2015)
  3. P. Kumam, "A hybrid iterative scheme for equilibrium problems and fixed point problems of asymptotically k-strict pseudo-contractions", J. Comp. Appl. Math., 233, pp.2013~2026 (2010)[DOI]
  4. G. Marino, "Weak and strong convergence theorems for strict pseudo- contractions in Hilbert space", J. Math. Anal. Appl., 329, pp.336~346 (2007)[DOI]
  5. C. Martinez-Yanes, "Strong convergence of the CQ method for fixed point iteration processes", Nonlinear Anal., 64, pp.2400~2411 (2006)[DOI]
  6. A. Moudafi, "Proximal and dynamical approaches to equilibrium problems", Lecture Notes in Economics and Mathematical Systems, 477 (1999)
  7. M.O. Osilike, "Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations", Comput. Math. Appl., 40, pp.559~567 (2000)[DOI]
  8. X. Qin, "A hybrid iterative scheme for asymptotically k-strictly pseudo-contractions in Hilbert spaces", Nonlinear Anal., 281, pp.516~524 (2003)

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