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General variational inclusions and General resolvent equations

강신민|엄정석|Zeqing Liu
대한수학회 (The Korean Mathematical Society)|2004.05|대한수학회보 (Bulletin of the KMS)|제41권 제2호|pp. 241-256

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Abstract

In this paper, we introduce and study a new class ofvariational inclusions, called the general variational inclusion.We prove the equivalence between the general variationalinclusions, the general resolvent equations, and the fixed-pointproblems, using the resolvent operator technique. This equivalenceis used to suggest and analyze a few iterative algorithms forsolving the general variational inclusions and the generalresolvent equations. Under certain conditions, the convergenceanalyses are also studied. The results presentedin this paper generalize, improve and unify anumber of recent results.

참고문헌 (8)

  1. "Moudafi \paper A perturbedalgorithm for variational inclusions \jour J"
  2. "paper Resolvent equations technique for variational inequalities", 4, pp.407~418 (1997)
  3. "An implicit method for mixed variational inequalities", 11, pp.109~113 (1998)
  4. "Generalized set-valued variational inclusions and resolvent equations", 228, pp.206~220 (1998)
  5. "paper Multivalued variational inequalities and resolvent equations", 26, pp.~121 (1997)
  6. "Rassias \paper Set-valued resolvent equations and mixed variational inequalities", 220, pp.741~759 (1998)
  7. "Generalized variational inequalities involving multivalued relaxed monotone operators", 10, pp.107~109 (1997)
  8. "On generalized variational inequalities involving relaxed Lipschitz and relaxed monotone operators", 213, pp.387~392 (1997)

관련 논문AI추천

A system of nonlinear variational inclusions in real Banach spacesChuan-Zhi Bai, Jin-Xuan Fang대한수학회 · 대한수학회보2003 · 제40권 제3호Parametric generalized mixed implicit quasi-variational inclusions박종열, 정재욱대한수학회 · 대한수학회지2007 · 제44권 제4호Generalized Set-valued Strongly Nonlinear Variational Inequalities in Banach SpacesK. H. Kim, N. J. Huang, Y. J. Cho, Y. P. Fang대한수학회 · 대한수학회지2003 · 제40권 제2호On solvability and Algorithm of General Strongly Nonlinear Variational-like Inequalities강신민, 심수학, Juhe Sun, Zeqing Liu대한수학회 · 대한수학회보2006 · 제43권 제2호On the Generalized Set-Valued Mixed Variational InequalitiesShin Min Kang, Yali Zhao, Zeqing Liu대한수학회 · 대한수학회논문집2003 · 제18권 제3호Generalized nonlinear multivalued mixedquasi-variational-like inequalities이병수, M. Firdosh Khan, Salahuddin대한수학회 · 대한수학회논문집2006 · 제21권 제4호

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