4.3 Article

HYBRID VISCOSITY EXTRAGRADIENT METHOD FOR SYSTEMS OF VARIATIONAL INEQUALITIES, FIXED POINTS OF NONEXPANSIVE MAPPINGS, ZERO POINTS OF ACCRETIVE OPERATORS IN BANACH SPACES

Journal

FIXED POINT THEORY
Volume 19, Issue 2, Pages 487-+

Publisher

HOUSE BOOK SCIENCE-CASA CARTII STIINTA
DOI: 10.24193/fpt-ro.2018.2.39

Keywords

Hybrid viscosity extragradient method; general system of variational inequalities; accretive operator; nonexpansive mapping

Funding

  1. Innovation Program of Shanghai Municipal Education Commission [15ZZ068]
  2. Ph.D. Program Foundation of Ministry of Education of China [20123127110002]
  3. Program for Outstanding Academic Leaders in Shanghai City [15XD1503100]
  4. [MOST 106-2923-E-039-001-MY3]

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In this paper, we introduce a hybrid viscosity extragradient method for a general system of variational inequalities with solutions being also common fixed points of a countable family of nonexpansive mappings and zeros point of an accretive operator in real smooth Banach spaces. Under quite appropriate assumptions, we obtain some strong convergence results which improve and develop the corresponding results in the literature.

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