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The Hybrid Projection Methods for Pseudocontractive, Nonexpansive Semigroup, and Monotone Mapping

Author

Listed:
  • Phayap Katchang
  • Somyot Plubtieng

Abstract

We modify the three‐step iterative schemes to prove the strong convergence theorems by using the hybrid projection methods for finding a common element of the set of solutions of fixed points for a pseudocontractive mapping and a nonexpansive semigroup mapping and the set of solutions of a variational inequality problem for a monotone mapping in a Hilbert space under some appropriate control conditions. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.

Suggested Citation

  • Phayap Katchang & Somyot Plubtieng, 2014. "The Hybrid Projection Methods for Pseudocontractive, Nonexpansive Semigroup, and Monotone Mapping," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:813701
    DOI: 10.1155/2014/813701
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    References listed on IDEAS

    as
    1. Lu-Chuan Ceng & Chi-Ming Chen & Ching-Feng Wen & Chin-Tzong Pang, 2014. "Relaxed Iterative Algorithms for Generalized Mixed Equilibrium Problems with Constraints of Variational Inequalities and Variational Inclusions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-25, March.
    2. Lu-Chuan Ceng & Juei-Ling Ho, 2014. "Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. H. Zegeye & N. Shahzad, 2013. "Extragradient Method for Solutions of Variational Inequality Problems in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, July.
    4. Lu-Chuan Ceng & Saleh Abdullah Al-Mezel & Qamrul Hasan Ansari, 2013. "Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, November.
    5. Li-Jun Zhu, 2013. "Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    6. Lu-Chuan Ceng & Ching-Feng Wen, 2013. "Hybrid Extragradient Methods for Finding Zeros of Accretive Operators and Solving Variational Inequality and Fixed Point Problems in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-27, September.
    7. Lu-Chuan Ceng & Juei-Ling Ho, 2014. "Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-27, February.
    8. H. Zegeye & N. Shahzad, 2013. "Extragradient Method for Solutions of Variational Inequality Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. Li-Jun Zhu, 2013. "Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    10. Lu-Chuan Ceng & Ching-Feng Wen, 2013. "Hybrid Extragradient Methods for Finding Zeros of Accretive Operators and Solving Variational Inequality and Fixed Point Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Lu-Chuan Ceng & Chi-Ming Chen & Ching-Feng Wen & Chin-Tzong Pang, 2014. "Relaxed Iterative Algorithms for Generalized Mixed Equilibrium Problems with Constraints of Variational Inequalities and Variational Inclusions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    12. Lu-Chuan Ceng & Saleh Abdullah Al-Mezel & Qamrul Hasan Ansari, 2013. "Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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