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A-Monotonicity and Its Role in Nonlinear Variational Inclusions

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  • R. U. Verma

    (University of Akron)

Abstract

The notion of A-monotonicity in the context of solving a new class of nonlinear variational inclusion problems is presented. Since A-monotonicity generalizes not only the well-explored maximal monotone mapping, but also a recently introduced and studied notion of H-monotone mapping, the results thus obtained are general in nature.

Suggested Citation

  • R. U. Verma, 2006. "A-Monotonicity and Its Role in Nonlinear Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 457-467, June.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:3:d:10.1007_s10957-006-9079-7
    DOI: 10.1007/s10957-006-9079-7
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    References listed on IDEAS

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    1. X. P. Ding & C. L. Luo, 1999. "On Parametric Generalized Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 195-205, January.
    2. R. U. Verma, 2004. "Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 203-210, April.
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    Cited by:

    1. Ram U. Verma, 2012. "General Class of Implicit Variational Inclusions and Graph Convergence on A-Maximal Relaxed Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 196-214, October.
    2. R. P. Agarwal & R. U. Verma, 2010. "Inexact A-Proximal Point Algorithm and Applications to Nonlinear Variational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 431-444, March.
    3. R. P. Agarwal & R. U. Verma, 2009. "Role of Relative A-Maximal Monotonicity in Overrelaxed Proximal-Point Algorithms with Applications," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 1-15, October.

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