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System of Nonlinear Set‐Valued Variational Inclusions Involving a Finite Family of H(·, ·)‐Accretive Operators in Banach Spaces

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  • Prapairat Junlouchai
  • Somyot Plubtieng

Abstract

We study a new system of nonlinear set‐valued variational inclusions involving a finite family of H(·, ·)‐accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of H(·, ·)‐accretive operators, we prove the existence of the solution for the system of nonlinear set‐valued variational inclusions. Moreover, we introduce a new iterative scheme and prove a strong convergence theorem for finding solutions for this system.

Suggested Citation

  • Prapairat Junlouchai & Somyot Plubtieng, 2012. "System of Nonlinear Set‐Valued Variational Inclusions Involving a Finite Family of H(·, ·)‐Accretive Operators in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:560248
    DOI: 10.1155/2012/560248
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    References listed on IDEAS

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    1. Ram U. Verma, 2004. "A -monotonicity and applications to nonlinear variational inclusion problems," International Journal of Stochastic Analysis, Hindawi, vol. 2004, pages 1-3, January.
    2. R. U. Verma, 2006. "General System of A-Monotone Nonlinear Variational Inclusion Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 151-157, October.
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