• Korean Journal of Mathematics
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• 제24권2호
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• pp.181-198
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• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

• Nonlinear Functional Analysis and Applications
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• 제29권3호
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• pp.867-883
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• 2024

The objective of this article is to study the general set-valued nonlinear variational-hemivariational inequalities and investigate the gap function, regularized gap function and Moreau-Yosida type regularized gap functions for the general set-valued nonlinear variational-hemivariational inequalities, and also discuss the error bounds for such inequalities using the characteristic of the Clarke generalized gradient, locally Lipschitz continuity, inverse strong monotonicity and Hausdorff Lipschitz continuous mappings.

• 충청수학회지
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• 제28권1호
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• pp.145-150
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• 2015

Aussel et al. [1] introduced the notion of inverse quasi-variational inequalities (IQVI) by combining quasi-variational inequalities and inverse variational inequalities. Discussions are made in a finite dimensional Euclidean space. In this note, we develop an infinite dimensional version of IQVI by investigating some basic properties of the regularized gap function of IQVI in a Banach space.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.183-191
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• 2007

In this paper, we introduce and study a new class of equilibrium problems, known as regularized mixed quasi equilibrium problems. We use the auxiliary principle technique to suggest and analyze some iterative schemes for regularized equilibrium problems. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving equilibrium problems and variational inequalities involving the convex sets.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.51-63
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• 2016

In this works, we consider a class of regularized equilibrium problems in Banach spaces. By using the auxiliary principle techniques to suggest some iterative schemes for regularized equilibrium problems and proved the convergence of these iterative methods required either pseudoaccretivity or partially relaxed strongly accretivity.

• 충청수학회지
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• 제27권2호
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• pp.271-276
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• 2014

Recently, Taji [7] and Harms et al. [4] studied the regularized gap function of QVI analogous to that of VI by Fukushima [2]. Discussions are made in a finite dimensional Euclidean space. In this note, an infinite dimensional generalization is considered in the framework of a reflexive Banach space. To do so, we introduce an extended quasi-variational inequality problem (in short, EQVI) and a generalized regularized gap function of EQVI. Then we investigate some basic properties of it. Our results may be regarded as an infinite dimensional extension of corresponding results due to Taji [7].

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.15-33
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• 2024

In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

• 대한기계학회논문집A
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• 제20권9호
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• pp.2887-2893
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• 1996

Governing equations infrictional contact problems are introduced using variational inequality formulations which are regularized to overcome the diffculties of non-differentiability of the friction functional. Also finite element approximations and a priori error estimations are derived based on those formulations. Numerical simulations are performed illustrating the theoretical results.