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Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators [PDF]
Mathematics, 2019 In this paper, we are interested in the pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in Hilbert spaces. An iterative algorithm has been constructed for finding a common solution of the pseudomonotone variational inequalities and fixed point of pseudocontractive operators.
Jen-Chih Yao +2 more
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The Pseudomonotone Polar for Multivalued Operators [PDF]
Optimization, 2017 In this work, we study the pseudomonotonicity of multivalued operators from the point of view of polarity, in an analogous way as the well-known monotone polar due to Martínez-Legaz and Svaiter, and the quasimonotone polar recently introduced by Bueno and Cotrina.
John Edwin Cotrina Asto, Orestes Bueno
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Multi-Valued Variational Inequalities With K-Pseudomonotone Operators
Journal of Optimization Theory and Applications, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J C Yao
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Existence of Zero Points for Pseudomonotone Operators in Banach Spaces
Journal of Global Optimization, 2008Based on the KKM principle by Ky Fan and on a minimax theorem of Kneser, the authors prove an existence result of zero points for pseudomonotone set-valued operators \(T:X\to 2^{E^*}\), where \(X\) is a nonempty closed convex subset of a Banach space \(E\).
Shin-Ya Matsushita, Wataru Takahashi
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Pseudomonotone Operators: A Survey of the Theory and Its Applications
Journal of Optimization Theory and Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicolas Hadjisavvas +2 more
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Variational Inequalities for (η, θ)-Pseudomonotone Operators in Nonreflexive Banach Spaces
Applied Mathematics Letters, 1999 The paper concerns a variational problem: Find \(x_0\in K\) such that, for all \(x\in K\), \(\langle Tx_0,\eta(x,x_0)\rangle\geq 0\). Here \(X\) is a nonreflexive Banach space, \(K\subseteq X^{**}\) is a convex set, \(T:K\to X^{*}\) is a hemicontinuous operator, and \(\eta:K\times K\to X^{**}\) is an appropriate substitute for the standard operator ...
Lee, B.-S., Lee, G.-M.
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A new inertial-based method for solving pseudomonotone operator equations with application
Computational and Applied Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sani Aji +4 more
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Nonlinear Analysis: Theory, Methods & Applications, 2011
In this paper, a solution existence theorem for a generalized variational inequality problem with an operator which is defined on an infinite-dimensional space is given. By using a new technique which reduces infinite variational inequality problems to finite ones, the proof of the theorem is provided.
G M Lee
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In this paper, a solution existence theorem for a generalized variational inequality problem with an operator which is defined on an infinite-dimensional space is given. By using a new technique which reduces infinite variational inequality problems to finite ones, the proof of the theorem is provided.
G M Lee
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Generalized Variational Inequalities with Pseudomonotone Operators Under Perturbations
Journal of Optimization Theory and Applications, 1999Variational inequalities and generalized variational inequalities with perturbed operators and constraints are considered and convergence of solutions to such problems is proved under an assumption of pseudomonotonicity. The paper extends previous results given by the authors proved in the setting of monotone operators.
LIGNOLA, MARIA BEATRICE +1 more
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Journal of Optimization Theory and Applications, 2001
The notion of exceptional family of elements for a set-valued mapping \(f\) on a Hilbert space \(H\), with respect to a closed pointed convex cone \(K\) in \(H\), is introduced. The main result of the paper shows that, for a set-valued pseudo-monotone mapping \(f\) on \(H\), the solvability of a complementary problem defined by \(f\) and \(K\) is ...
V V Kalashnikov, G Isac
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The notion of exceptional family of elements for a set-valued mapping \(f\) on a Hilbert space \(H\), with respect to a closed pointed convex cone \(K\) in \(H\), is introduced. The main result of the paper shows that, for a set-valued pseudo-monotone mapping \(f\) on \(H\), the solvability of a complementary problem defined by \(f\) and \(K\) is ...
V V Kalashnikov, G Isac
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