Iterative algorithms for generalized monotone variational inequalities

Noor, Muhammad Aslam

doi:10.1007/bf02941909

Cited by 6 publications

(6 citation statements)

References 11 publications

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“…We will also work with the next fuzzy model: [15] introduced the notion of a random variational inequality. We propose the next random system of quasi-variational inequalities which generalizes the random one studied, for instance, by Yuan in [26].…”

Section: New Types Of Systems Of Generalized Quasi-variational Inequamentioning

confidence: 99%

On a New Class of Systems of Generalized Quasi-Variational Inequalities

Patriche

2014

Numerical Functional Analysis and Optimization

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We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.Keywords: system of generalized quasi-variational inequalities, free abstract economies, fuzzy games, random equilibria, random variational inequalities.

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Section: New Types Of Systems Of Generalized Quasi-variational Inequamentioning

confidence: 99%

On a New Class of Systems of Generalized Quasi-Variational Inequalities

Patriche

2014

Numerical Functional Analysis and Optimization

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“…Since then several classes of variational inequalities in the deterministic and fuzzy setting have been studied (see, for example, ). Next, in 1993, the notion of a random variational inequality was introduced by Noor and Elsanousi . Very recently, Patriche applied the model of the Bayesian abstract fuzzy economy in order to prove the existence of solution for the two types of random quasi‐variational inequalities with random fuzzy mappings.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy games for a general Bayesian abstract fuzzy economy model of product measurable spaces

Saipara

2015

Math Methods in App Sciences

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In this paper, we introduce a general Bayesian abstract fuzzy economy model of product measurable spaces, and we prove the existence of Bayesian fuzzy equilibrium for this model. Our results extend and improve the corresponding recent results announced by Patriche and many authors from the literature. It captures the idea that the uncertainties characterize the individual feature of the decisions of the agents involved in different economic activities. In this paper, the uncertainties can be described by using random fuzzy mappings. Further attention is needed for the study of applications of the established result in the game theory and the fuzzy economic field.

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“…Since then, this domain has been extensively developed and has been found very useful in many diverse fields of pure and applied sciences, such as mechanics, physics, optimization and control theory, operations research and several branches of engineering sciences. Recently, the random variational inequalities have been introduced and studied in [7], [8], [15], [26], [30]. We prove the existence of the solutions for systems of random generalized quasi-variational inequalities with random fuzzy mappings which we define.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy games with a countable space of actions and applications to systems of generalized quasi-variational inequalities

Patriche

2014

Fixed Point Theory Appl

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We introduce an abstract fuzzy economy (generalized fuzzy game) model with a countable space of actions, and we study the existence of fuzzy equilibrium. As application, we prove the existence of solutions for the systems of generalized quasi-variational inequalities with random fuzzy mappings, defined in this paper. Our results bring novelty to the current literature by considering random fuzzy mappings whose values are fuzzy sets over complete countable metric spaces.

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Iterative algorithms for generalized monotone variational inequalities

Cited by 6 publications

References 11 publications

On a New Class of Systems of Generalized Quasi-Variational Inequalities

On a New Class of Systems of Generalized Quasi-Variational Inequalities

Fuzzy games for a general Bayesian abstract fuzzy economy model of product measurable spaces

Fuzzy games with a countable space of actions and applications to systems of generalized quasi-variational inequalities

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