DOI QR코드

DOI QR Code

Iterative Algorithm for a New System of Variational Inclusions with B-monotone Operators in Banach Spaces

Lee, Sang Keun;Jeong, Jae Ug

  • Received : 2010.11.22
  • Accepted : 2013.04.02
  • Published : 2013.09.23

Abstract

In this paper, we introduce and study a new system of variational inclusions with B-monotone operators in Banach spaces. By using the proximal mapping associated with B-monotone operator, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm for this system of variational inclusions. The results presented in this paper extend and improve some known results in the literature.

Keywords

B-monotone operator;Proximal mapping;Iterative algorithm;Variational inclusion;Convergence

References

  1. C. Baiocchi and A. Capelo, Variational and Quasi-Variational Inequalities, J. Wiley and Sons, New York, 1984.
  2. H. Brezis, Operateur Maximauz Monotone et Semigroupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973.
  3. R. W. Cottle, F. Giannessi and J. L. Lions, Variational Inequalities: Theory and Applications, J. Wiley and Sons, New York, 1980.
  4. J. Crank, Free and Moving Boundary Problems, Clarendon Press, Oxford, U.K. 1984.
  5. V. F. Demyanov, G. E. Stavroulakis, L. N. Polyakova and P. D. Panagiotopoulos, Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics, Kluwer Academic Publications, Holland, 1996.
  6. X. P. Ding and H. R. Feng, Algorithm for solving a new class of generalized nonlinear implicit quasi-variational inclusions in Banach spaces, Appl. Math. Comput., 208(2009), 547-555. https://doi.org/10.1016/j.amc.2008.12.028
  7. G. Duvaut and J. L. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976.
  8. Y. P. Fang and N. J. Huang, H-monotone operator and resolvent operator technique for variational inclusions, Appl. Math. Comput., 145(2003), 795-803. https://doi.org/10.1016/S0096-3003(03)00275-3
  9. Xue-ping Luo and Nan-jing Huang, A new class of variational inclusions with Bmonotone operators in Banach spaces, J. Comput. Appl. Math., 233(2010), 1888-1896. https://doi.org/10.1016/j.cam.2009.09.025
  10. S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30(1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475
  11. F. Q. Xia and N. J. Huang, Variational inclusions with a general H-monotone operator in Banach spaces, Comput. Math. Appl., 54(2007), 24-30. https://doi.org/10.1016/j.camwa.2006.10.028