A hybrid scheme for finite families of equilibrium, variational inequality and fixed point problems

  • Zegeye H
  • Shahzad N
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Abstract

We introduce an iterative process for finding an element in the common fixed point set of finite family of closed relatively quasi-nonexpansive mappings, common solutions of finite family of equilibrium problems and common solutions of finite family of variational inequality problems for monotone mappings in Banach spaces. Our theorem extends and unifies most of the results that have been proved for this important class of nonlinear operators. © 2010 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Equilibrium problems
  • Monotone mappings
  • Relatively quasi-nonexpansive mappings
  • Strong convergence
  • Strongly monotone mappings
  • Variational inequality problems
  • γ-inverse strongly monotone mappings

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