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Approximation of Common Fixed Points of a Sequence of Nearly Nonexpansive Mappings and Solutions of Variational Inequality Problems

Author

Listed:
  • D. R. Sahu
  • Shin Min Kang
  • Vidya Sagar

Abstract

We introduce an explicit iterative scheme for computing a common fixed point of a sequence of nearly nonexpansive mappings defined on a closed convex subset of a real Hilbert space which is also a solution of a variational inequality problem. We prove a strong convergence theorem for a sequence generated by the considered iterative scheme under suitable conditions. Our strong convergence theorem extends and improves several corresponding results in the context of nearly nonexpansive mappings.

Suggested Citation

  • D. R. Sahu & Shin Min Kang & Vidya Sagar, 2012. "Approximation of Common Fixed Points of a Sequence of Nearly Nonexpansive Mappings and Solutions of Variational Inequality Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:902437
    DOI: 10.1155/2012/902437
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    References listed on IDEAS

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    1. Shuang Wang, 2012. "Two General Algorithms for Computing Fixed Points of Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, May.
    2. Shuang Wang, 2012. "Two General Algorithms for Computing Fixed Points of Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Ibrahim Karahan & Murat Ozdemir, 2014. "Convergence Theorems for Hierarchical Fixed Point Problems and Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. M. De la Sen, 2013. "Some Results on Fixed and Best Proximity Points of Precyclic Self‐Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. M. De la Sen & E. Karapinar, 2013. "Best Proximity Points of Generalized Semicyclic Impulsive Self‐Mappings: Applications to Impulsive Differential and Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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