Journal ArticleDOI
H-Monotone operator and resolvent operator technique for variational inclusions
Ya-Ping Fang,Nan-Jing Huang +1 more
TLDR
The resolvent operator associated with an H-monotone operator is defined and its Lipschitz continuity is presented and a new algorithm for solving this class of variational inclusions by using the resolent operator technique is constructed.About:
This article is published in Applied Mathematics and Computation.The article was published on 2003-12-01. It has received 194 citations till now. The article focuses on the topics: Resolvent formalism & Pseudo-monotone operator.read more
Citations
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Journal ArticleDOI
A new system of variational inclusions with (H, η )-monotone operators in hilbert spaces
TL;DR: In this article, a new system of variational inclusions involving (H, @h)-monotone operators in Hilbert space is introduced and studied, and a new algorithm for approximating the solution of this system is presented.
Journal ArticleDOI
Nonlinear relaxed cocoercive variational inclusions involving (A, η )-accretive mappings in banach spaces
TL;DR: A new concept of (A, @h)-accretive mappings is introduced, which generalizes the existing monotone or accretive operators and construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed Cocoercive variational inclusions in q-uniformly smooth Banach spaces.
Journal ArticleDOI
On a new system of nonlinear A-monotone multivalued variational inclusions ✩
TL;DR: In this article, a new iterative algorithm for solving nonlinear multivalued variational inclusions associated with A-monotone mappings in Hilbert spaces is presented. And the authors also prove the existence of solutions for the nonlinear multi-valued variational infinities and the convergence of iterative sequences generated by the algorithm.
Journal ArticleDOI
Characterization of H-monotone operators with applications to variational inclusions
TL;DR: In this article, necessary and sufficient conditions for operators to be H-monotone are established and a new iterative algorithm for solving a class of variational inclusions is introduced.
Journal ArticleDOI
Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A,η)-monotone mappings
TL;DR: In this article, a new class of nonlinear set-valued variational inclusions involving ( A, η ) -monotone mappings in a Hilbert space setting is introduced, and based on the generalized resolvent operator technique associated with ( A, η) -monotonicity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.
References
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Journal ArticleDOI
Numerical Methods for Nonlinear Variational Problems
Roland Glowinski,J. T. Oden +1 more
Journal ArticleDOI
Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications
Patrick T. Harker,Jong-Shi Pang +1 more
TL;DR: The field of finite-dimensional variational inequality and complementarity problems has seen a rapid development in its theory of existence, uniqueness and sensitivity of solution(s), in the theory of algorithms, and in the application of these techniques to transportation planning, regional science, socio-economic analysis, energy modeling, and game theory as mentioned in this paper.
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H-Accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces
Ya-Ping Fang,Nan-Jing Huang +1 more