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A -monotonicity and applications to nonlinear variational inclusion problems

Author

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  • Ram U. Verma

Abstract

A new notion of the A -monotonicity is introduced, which generalizes the H -monotonicity. Since the A -monotonicity originates from hemivariational inequalities, and hemivariational inequalities are connected with nonconvex energy functions, it turns out to be a useful tool proving the existence of solutions of nonconvex constrained problems as well.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnijsa:276430
    DOI: 10.1155/S1048953304403013
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    Cited by:

    1. Ting-jian Xiong & Heng-you Lan, 2014. "Iterative Algorithms for New General Systems of Set‐Valued Variational Inclusions Involving (A, η)‐Maximal Relaxed Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Pongsakorn Sunthrayuth & Poom Kumam, 2011. "A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    3. Bijaya Kumar Sahu & Sujeet Kumar & Sabyasachi Pani, 2023. "An auxiliary problem principle for the solutions of mixed invex equilibrium problems in Banach spaces," OPSEARCH, Springer;Operational Research Society of India, vol. 60(4), pages 1777-1792, December.
    4. Zhongping Wan & Jia-Wei Chen & Hai Sun & Liuyang Yuan, 2011. "A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    5. 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).
    6. Jittiporn Suwannawit & Narin Petrot, 2012. "Existence and Stability of Iterative Algorithm for a System of Random Set‐Valued Variational Inclusion Problems Involving (A, m, η)‐Generalized Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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