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Convergence of a Hybrid Iterative Scheme for Fixed Points of Nonexpansive Maps, Solutions of Equilibrium, and Variational Inequalities Problems

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  • Bashir Ali

Abstract

Let be a closed, convex, and nonempty subset of a real -uniformly smooth Banach space , which is also uniformly convex. For some , let and be family of nonexpansive maps and -inverse strongly accretive map, respectively. Let be a bifunction satisfying some conditions. Let be a nonexpansive projection of onto . For some fixed real numbers , , and arbitrary but fixed vectors , let and be sequences generated by , , , , , where is fixed, and are sequences satisfying appropriate conditions. If , under some mild conditions, we prove that the sequences and converge strongly to some element in .

Suggested Citation

  • Bashir Ali, 2013. "Convergence of a Hybrid Iterative Scheme for Fixed Points of Nonexpansive Maps, Solutions of Equilibrium, and Variational Inequalities Problems," Journal of Mathematics, Hindawi, vol. 2013, pages 1-11, March.
  • Handle: RePEc:hin:jjmath:370143
    DOI: 10.1155/2013/370143
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