A posteriori bounds of approximate solution to variational and quasi-variational inequalities

Jacimovic, Milojica; Krnic, Izedin

doi:10.2298/fil1101163j

Cited by 2 publications

(1 citation statement)

References 7 publications

(18 reference statements)

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“…(3) For more details on variational inequalities and quasi-variational inequalities, completely generalized multi-valued co-variational inequalities, generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings and others, refer to [1], [16] and [17].…”

Section: Existence Theorems For Generalized Bi-complementarity Problementioning

confidence: 99%

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators in non-compact settings

Chowdhury

Cho

2016

Filomat

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In this paper, we introduce a new class of generalized bi-quasi-variational inequalities for quasipseudo-monotone type II operators in non-compact settings of locally convex Hausdorff topological vector spaces and show the existence results of solutions for generalized bi-quasi-variational inequalities. Our results improve, extend and generalized the corresponding results given by some authors. The generalized bi-quasi-variational inequality problem was first introduced by Shih and Tan [19] in 1989. The following is the definition due to Shih and Tan [19]. Definition 1.1. Let E and F be vector spaces over Φ, •, • : F × E → Φ be a bilinear functional and be X a nonempty subset of E. If S : X → 2 X and M, T : X → 2 F are set-valued mappings, then the generalized bi-quasi variational inequality problem for the triple (S, M, T) is to findŷ ∈ X satisfying the following properties: (1)ŷ ∈ S(ŷ); (2) inf w∈T(ŷ) Re f − w,ŷ − x ≤ 0 for all x ∈ S(ŷ) and f ∈ M(ŷ). In this definition, for any nonempty set X, 2 X denote the class or family of all nonempty subsets of X. Also, we use F (X) to denote the family of all nonempty finite subsets of X. Moreover, throughout this paper, Φ denotes either the real field R or the complex field C.

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Section: Existence Theorems For Generalized Bi-complementarity Problementioning

confidence: 99%

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators in non-compact settings

Chowdhury

Cho

2016

Filomat

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Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type I operators on non-compact sets

Chowdhury

Tan

2010

Computers & Mathematics with Applications

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A posteriori bounds of approximate solution to variational and quasi-variational inequalities

Cited by 2 publications

References 7 publications

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators in non-compact settings

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators in non-compact settings

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type I operators on non-compact sets

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