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New Hybrid Steepest Descent Algorithms for Equilibrium Problem and Infinitely Many Strict Pseudo‐Contractions in Hilbert Spaces

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  • Peichao Duan

Abstract

We propose an explicit iterative scheme for finding a common element of the set of fixed points of infinitely many strict pseudo‐contractive mappings and the set of solutions of an equilibrium problem by the general iterative method, which solves the variational inequality. In the setting of real Hilbert spaces, strong convergence theorems are proved. The results presented in this paper improve and extend the corresponding results reported by some authors recently. Furthermore, two numerical examples are given to demonstrate the effectiveness of our iterative scheme.

Suggested Citation

  • Peichao Duan, 2013. "New Hybrid Steepest Descent Algorithms for Equilibrium Problem and Infinitely Many Strict Pseudo‐Contractions in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:139123
    DOI: 10.1155/2013/139123
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    References listed on IDEAS

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    1. Peichao Duan & Aihong Wang, 2012. "General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Peichao Duan & Aihong Wang, 2012. "General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, May.
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