• Title/Summary/Keyword: strictly pseudo-contractive mapping

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Convergence of an Iterative Algorithm for Systems of Variational Inequalities and Nonlinear Mappings in Banach Spaces

  • JEONG, JAE UG
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.933-951
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    • 2015
  • In this paper, we consider the problem of convergence of an iterative algorithm for a general system of variational inequalities, a nonexpansive mapping and an ${\eta}$-strictly pseudo-contractive mapping. Strong convergence theorems are established in the framework of real Banach spaces.

SOLUTIONS OF SYSTEMS OF VARIATIONAL INEQUALITIES ON FIXED POINTS OF NONEXPANSIVE MAPPINGS

  • Piri, Hossein
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.621-640
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    • 2014
  • In this paper, we introduce a new approximating method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solution of system variational inequalities for finite family of inverse strongly monotone mappings and strictly pseudo-contractive of Browder-Petryshyn type mappings. We show that the sequence converges strongly to a common element the above two sets under some parameter controling conditions. Our results improve and extend the results announced by many others.

A HYBRID PROJECTION METHOD FOR RELAXED COCOERCIVE MAPPINGS AND STRICTLY PSEUDO-CONTRACTIVE MAPPINGS

  • Liu, Ying
    • East Asian mathematical journal
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    • v.28 no.3
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    • pp.305-320
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    • 2012
  • The purpose of this paper is to introduce a hybrid projection method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inclusion problem and the set of common fixed points of a finite family of strict pseudo-contractions in Hilbert spaces.

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

  • Kim, Seung-Hyun;Kang, Mee-Kwang
    • The Pure and Applied Mathematics
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    • v.25 no.2
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    • pp.149-160
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    • 2018
  • In this paper, we prove a strong convergence result under an iterative scheme for N finite asymptotically $k_i-strictly$ pseudo-contractive mappings and a firmly nonexpansive mappings $S_r$. Then, we modify this algorithm to obtain a strong convergence result by hybrid methods. Our results extend and unify the corresponding ones in [1, 2, 3, 8]. In particular, some necessary and sufficient conditions for strong convergence under Algorithm 1.1 are obtained.