Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A SYSTEM OF NONLINEAR SET-VALUED IMPLICIT VARIATIONAL INCLUSIONS IN REAL BANACH SPACES

  • Bai, Chuanzhi (Department of Mathematics, Huaiyin Normal University) ;
  • Yang, Qing (Department of Mathematics, Huaiyin Normal University)
  • Published : 2010.01.31
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Abstract

In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

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References

  1. C. Z. Bai and J. X. Fang, A system of nonlinear variational inclusions in real Banach spaces, Bull. Korean Math. Soc. 40 (2003), no. 3, 385–397. https://doi.org/10.4134/BKMS.2003.40.3.385
  2. S. S. Chang, H. W. Joseph Lee, and C. K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007), no. 3, 329–334. https://doi.org/10.1016/j.aml.2006.04.017
  3. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
  4. Y. P. Fang and N. J. Huang, H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces, Appl. Math. Lett. 17 (2004), no. 6, 647–653. https://doi.org/10.1016/S0893-9659(04)90099-7
  5. Y. P. Fang and N. J. Huang, H-Monotone operator and resolvent operator technique for variational inclusions, Appl. Math. Comput. 145 (2003), no. 2-3, 795–803. https://doi.org/10.1016/S0096-3003(03)00275-3
  6. H. Nie, Z. Liu, K. H. Kim, and S. M. Kang, A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings, Adv. Nonlinear Var. Inequal. 6 (2003), no. 2, 91–99.
  7. M. Aslam Noor, Three-step iterative algorithms for multivalued quasi variational inclusions, J. Math. Anal. Appl. 255 (2001), no. 2, 589–604. https://doi.org/10.1006/jmaa.2000.7298
  8. R. U. Verma, Generalized system for relaxed cocoercive variational inequalities and its projection methods, J. Optim. Theory Appl. 121 (2004), no. 1, 203–210. https://doi.org/10.1023/B:JOTA.0000026271.19947.05
  9. R. U. Verma, General convergence analysis for two-step projection methods and applications to variational problem, Appl. Math. Lett. 18 (2005), no. 11, 1286–1292. https://doi.org/10.1016/j.aml.2005.02.026
  10. H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16 (1991), no. 12, 1127–1985. https://doi.org/10.1016/0362-546X(91)90200-K

Cited by

  1. Algorithm for Solving a New System of Generalized Variational Inclusions in Hilbert Spaces vol.2013, 2013, https://doi.org/10.1155/2013/461371