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On Strongly Nonlinear Implicit Complementarity Problems in Hilbert Spaces

Nan-Jing Huang|Yeol Je Cho
경북대학교 자연과학대학 수학과|2006.03|Kyungpook Mathematical Journal|제46권 제1호|pp. 145-152

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Abstract

In this paper, we study a class of strongly nonlinear implicit complementarityproblems in the setting of Hilbert spacesH (not necessarily Hilbert lattices). By usingthe property of the projection and a suitable change of variables, we establish the equiva-lence between the strongly nonlinear implicit complementarity problem and the xed pointproblem in H. Moreover, we use this equivalence and the xed point theorem of Boyd and Wong toprove the existence and uniqueness of solutions for the strongly nonlinear implicit comple-mentarity problem in H .

참고문헌 (12)

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  5. "Complementarity and variational problems", 19, pp.177~208 (1976)
  6. "Complementarity pivot theory of mathematical pro-gramming", 1, pp.163~185 (1968)
  7. "Lecture Notes in Math." (1992), Springer-Verlag
  8. "Bimatrix equilibrium points and mathematical programming", 1965, pp.11 (1964), 681~689
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  12. "Projections on convex sets in Hilbert space and spectral theory in ``Contribution to Nonlinear Functional Analysis", pp.237 237~424 424 (1971), Academic Press Academic Press

관련 논문AI추천

Some vector implicit complementarity problems with corresponding variational inequality problems강미광대한수학회 · 대한수학회논문집2007 · 제22권 제3호On solvability and Algorithm of General Strongly Nonlinear Variational-like Inequalities강신민, 심수학, Juhe Sun, Zeqing Liu대한수학회 · 대한수학회보2006 · 제43권 제2호Generalized Set-valued Strongly Nonlinear Variational Inequalities in Banach SpacesK. H. Kim, N. J. Huang, Y. J. Cho, Y. P. Fang대한수학회 · 대한수학회지2003 · 제40권 제2호GENERALIZED F-IMPLICIT MULTIVALUED VARIATIONAL INEQUALITY PROBLEMS AND COMPLEMENTARITY PROBLEMS이병수, M. Firdosh Khan, Salahuddin영남수학회 · East Asian Mathematical Journal2010 · 제26권 제3호A new system of generalized nonlinear mixedquasivariational inequalities and Iterative Algorithms in Hilbert spaces김경수, 김종규대한수학회 · 대한수학회지2007 · 제44권 제4호Existence and iterative approximations of solutions for strongly nonlinear variational-like inequalities강신민, Jinsong Li, Juhe Sun영남수학회 · East Asian Mathematical Journal2011 · 제27권 제5호

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