Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

GENERAL VARIATIONAL INCLUSIONS AND GENERAL RESOLVENT EQUATIONS

  • Liu, Zeqing (Department of Mathematics, Liaoning Normal University) ;
  • Ume, Jeong-Sheok (Department of Applied Mathematics, Changwon National University) ;
  • Kang, Shin-Min (Department of Mathematics And Research Institute of Natural Science, Gyeongsang National University)
  • Published : 2004.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.

Keywords

References

  1. Convex analysis and variational problems v.1 I.Ekeland;R.Temam
  2. J. Math. Anal. Appl. v.185 no.3 A perturbed algorithm for variatonal inclusions A.Hassouni;A.Moudafi https://doi.org/10.1006/jmaa.1994.1277
  3. Pacific J. Math. v.30 Multi-valued contraction mappings S.B.Nadler,Jr. https://doi.org/10.2140/pjm.1969.30.475
  4. Korean J. Comput. Appl. Math. v.4 no.2 Resolvent equations technique for variational inequalities M.A.Noor
  5. Appl. Math. Lett. v.11 no.4 An implicit method for mixed variational inequalities M.A.Noor
  6. J. Math. Anal. Appl. v.228 no.1 Generalized set-valued variational inclusions and resolvent equations M.A.Noor https://doi.org/10.1006/jmaa.1998.6127
  7. Math. Comput. Modelling v.26 no.7 Multivalued variational inequalities and resolvent equations M.A.Noor;K.I.Noor
  8. J. Math. Anal. Appl. v.220 no.2 Set-valued resolvent equations and mixed variational inequalities M.A.Noor;K.I.Noor;T.M.Rassias https://doi.org/10.1006/jmaa.1997.5893
  9. Appl. Math. Lett. v.10 no.4 Generalized variational inequalities involving multivalued relaxed monotone operators R.U.Verma
  10. J. Math. Anal. Appl. v.213 no.1 On generalized variational inequalities involving relaxed Lipschitz and relaxed monotone operators R.U.Verma https://doi.org/10.1006/jmaa.1997.5556

Cited by

  1. Auxiliary principle for generalized nonlinear variational-like inequalities vol.2006, 2006, https://doi.org/10.1155/IJMMS/2006/95723