scholarly journals Existence and Convergence Results for Generalized Mixed Quasi-Variational Hemivariational Inequality Problem

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1882
Author(s):  
Shih-Sen Chang ◽  
Salahuddin ◽  
Lin Wang ◽  
Gang Wang ◽  
Yunhe Zhao
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Hilbert Spaces ◽  
Hemivariational Inequalities ◽  
Convergence Problem ◽  
The Third ◽  
Convergence Results ◽  
Quasi Variational Inequality ◽  
Existence Of Optimal Control ◽  
The Relationship

The main purpose of this paper is threefold. One is to study the existence and convergence problem of solutions for a class of generalized mixed quasi-variational hemivariational inequalities. The second one is to study the existence of optimal control for such kind of generalized mixed quasi-variational hemivariational inequalities under given control u∈U. The third one is to study the relationship between the optimal control and the data for the underlying generalized mixed quasi-variational inequality problems and a class of minimization problem. As an application, we utilize our results to study the elastic frictional problem in a class of Hilbert spaces. The results presented in the paper extend and improve upon some recent results.

Error Bounds for Inverse Mixed Quasi-Variational Inequality via Generalized Residual Gap Functions

2021 ◽  
pp. 2150017
Author(s):  
Yinfeng Zhang ◽  
Guolin Yu
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Error Bounds ◽  
Feasible Solution ◽  
Variational Inequality Problem ◽  
Gap Functions ◽  
Strong Monotonicity ◽  
Mixed Variational Inequality ◽  
Related Literature ◽  
Quasi Variational Inequality

In this paper, we investigate error bounds of an inverse mixed quasi variational inequality problem in Hilbert spaces. Under the assumptions of strong monotonicity of function couple, we obtain some results related to error bounds using generalized residual gap functions. Each presented error bound is an effective estimation of the distance between a feasible solution and the exact solution. Because the inverse mixed quasi-variational inequality covers several kinds of variational inequalities, such as quasi-variational inequality, inverse mixed variational inequality and inverse quasi-variational inequality, the results obtained in this paper can be viewed as an extension of the corresponding results in the related literature.

scholarly journals Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

2016 ◽  
Vol 15 (1) ◽  
pp. 79-96
Author(s):  
Muhammad Aqeel Ahmad Khan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Finite Family ◽  
Common Element ◽  
Common Solution ◽  
Convergence Results ◽  
Generalized Equilibrium

AbstractIn this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.

scholarly journals Advanced Algorithms and Common Solutions to Variational Inequalities

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1198 ◽  
Author(s):  
Hasanen A. Hammad ◽  
Habib ur Rehman ◽  
Manuel De la Sen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Variational Inequality Problems ◽  
Gradient Algorithms ◽  
Convergence Results ◽  
Set Valued Mappings ◽  
And Performance

The paper aims to present advanced algorithms arising out of adding the inertial technical and shrinking projection terms to ordinary parallel and cyclic hybrid inertial sub-gradient extra-gradient algorithms (for short, PCHISE). Via these algorithms, common solutions of variational inequality problems (CSVIP) and strong convergence results are obtained in Hilbert spaces. The structure of this problem is to find a solution to a system of unrelated VI fronting for set-valued mappings. To clarify the acceleration, effectiveness, and performance of our parallel and cyclic algorithms, numerical contributions have been incorporated. In this direction, our results unify and generalize some related papers in the literature.

Control Strategy of Proportional Reinsurance with Dividend Process

2014 ◽  
Vol 488-489 ◽  
pp. 1301-1305
Author(s):  
Shi Liang Sun ◽  
Xiao Qian Huang ◽  
Lu Lian
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Control Strategy ◽  
Proportional Reinsurance ◽  
Insurance Company ◽  
Optimal Control Strategy ◽  
Return Function ◽  
Existence Of Optimal Control

This paper is concerned with the problem of proportional reinsurance control strategy with dividend process in insurance company. The existence of optimal control strategy is proved by variational inequality,and the specific construct of optimal control strategy and the explicit structure of optimal return function are derived.

scholarly journals Inertial S-type Tseng's extragradient Algorithm for solution of Variational Inequality problems

2021 ◽  
Author(s):  
D. R. Sahu ◽  
AMIT KUMAR SINGH
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Iteration Process ◽  
Variational Inequality Problems ◽  
Numerical Examples ◽  
Lipschitz Continuous ◽  
Mild Conditions ◽  
Extragradient Algorithm ◽  
Convergence Results ◽  
Continuous Operators

In this paper, we introduce inertial Tseng’s extragradient algorithms combined with normal-S iteration process for solving variational inequality problems involving pseudo-monotone and Lipschitz continuous operators. Under mild conditions, we establish the weak convergence results in Hilbert spaces. Numerical examples are also present to show that faster behaviour of the proposed method.

Retroaktive Neuverhandlung

2018 ◽  
Vol 63 (1) ◽  
Author(s):  
Daniel Martin Feige
Keyword(s):  
Original Work ◽  
The Other ◽  
Final Part ◽  
Critical Reading ◽  
The Third ◽  
Works Of Art ◽  
The Relationship

Der Beitrag widmet sich der Frage historischer Folgeverhältnisse in der Kunst. Gegenüber dem Gedanken, dass es ein ursprüngliches Werk in der Reihe von Werken gibt, das späteren Werken seinen Sinn gibt, schlägt der Text vor, das Verhältnis umgekehrt zu denken: Im Lichte späterer Werke wird der Sinn früherer Werke neu ausgehandelt. Dazu geht der Text in drei Schritten vor. Im ersten Teil formuliert er unter der Überschrift ›Form‹ in kritischer Abgrenzung zu Danto und Eco mit Adorno den Gedanken, dass Kunstwerke eigensinnig konstituierte Gegenstände sind. Die im Gedanken der Neuverhandlung früherer Werke im Lichte späterer Werke vorausgesetzte Unbestimmtheit des Sinns von Kunstwerken wird im zweiten Teil unter dem Schlagwort ›Zeitlichkeit‹ anhand des Paradigmas der Improvisation erörtert. Der dritte und letzte Teil wendet diese improvisatorische Logik unter dem Label ›Neuaushandlung‹ dann dezidiert auf das Verhältnis von Vorbild und Nachbild an. The article proposes a new understanding of historical succession in the realm of art. In contrast to the idea that there is an original work in the series of works that gives meaning to the works that come later, the text proposes to think it exactly the other way round: in the light of later works, the meanings of earlier works are renegotiated. The text proceeds in three steps to develop this idea. Under the heading ›Form‹ it develops in the first part a critical reading of Danto’s and Eco’s notion of the constitution of the artworks and argues with Adorno that each powerful work develops its own language. In the second part, the vagueness of the meaning of works of art presupposed in the idea of renegotiating earlier works in the light of later works is discussed under the term ›Temporality‹ in terms of the logic of improvisation. The third and final part uses this improvisational logic under the label ›Renegotiation‹ to understand the relationship between model and afterimage in the realm of art.

RECREATION SPECIALIZATION FOR RUNNERS AND EVENT ATTACHMENT

2020 ◽  
Author(s):  
Isao Okayasu ◽  
Chi-Ok Oh ◽  
Duarte B Morais
Keyword(s):  
Practical Implication ◽  
Event Management ◽  
Attitudes And Behaviors ◽  
The Third ◽  
Study Results ◽  
The World ◽  
Recreation Specialization ◽  
And Behaviors ◽  
The Relationship ◽  
Predictive Relationship

Running is one of the most popular activities in the world. Runners’ attitudes and behaviors vary depending on their running style. This study aims to construct different measures of running specialization based on the theory of specialization. This study also tests a runner’s stage of specialization segmentation based on recreation specialization and examines the predictive relationship between a runner’s specialization and event attachment. Three groups of sampling data assess the performance of diverse specialization measures for running in three marathon events. First, two surveys were conducted with marathon participants to assess the performance of diverse specialization measures for runners. Second, the third dataset was used to examine the relationship between a runner’s recreation specialization and event attachment.The study results showed that the 15 measures of specialization showed a good fit to the data. Our research showed how runners’ recreation specialization is connected to their event attachment. In addition, this study suggested event management for subdivisions of runners. Its practical implication is that recreation specialization for running can help us understand event attachment.

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