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On generalized nonlinear variational-like inequality problems

Rais Ahmad, Syed Shakaib Irfan
2006 Applied Mathematics Letters  
In this work, we consider a generalized nonlinear variational-like inequality problem in the setting of locally convex topological vector spaces and prove the existence of its solutions.  ...  Introduction and preliminaries The variational-like inequality, also known as the pre-variational inequality, is one of the generalized forms of variational inequalities; see, for example, [2, [5] [6]  ...  In this work, we consider the generalized nonlinear variational-like inequality problem in the setting of locally convex topological vector spaces and prove the existence of its solution.  ... 
doi:10.1016/j.aml.2005.05.010 fatcat:cloot7nsgzeproomxafr32lxta

A Note on the Generalized Nonlinear Vector Variational-Like Inequality Problem

Ankit Gupta, Satish Kumar, Ratna Dev Sarma, Pankaj Kumar Garg, Reny George, Yuanfang Ru
2021 Journal of Function Spaces  
In this paper, we discuss two variants of the generalized nonlinear vector variational-like inequality problem. We provide their solutions by adopting topological approach.  ...  nonlinear vector variational-like inequality problems.  ...  Then, the generalized nonlinear vector variational-like inequality problem (I) has a solution.  ... 
doi:10.1155/2021/4488217 fatcat:nymatzmspffpjflnncwd6nn6k4

Variational Inequalities and Vector Optimization 2014

Xian-Jun Long, Jian-Wen Peng, Nan-Jing Huang, Jen-Chih Yao
2014 Journal of Applied Mathematics  
, includes works on variational inequalities, equilibrium problems and nonexpansive mappings, vector optimization problems and generalized convex functions, robust optimization problems, and optimization  ...  Because of the importance and active impact of the variational inequality and the vector optimization problem in the nonlinear analysis and optimization, this special issue, focusing on most recent contributions  ...  Acknowledgments The editors of this special issue would like to express their gratitude to the authors who have submitted their papers for consideration and to the expert referees who provided them with  ... 
doi:10.1155/2014/214957 fatcat:oe5dzr2eynb3vhuzn45pyshzni

Page 10027 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
As consequences of our main result, we give some ex- istence results for vector equilibrium problems, vector variational- like inequality problems and vector variational inequality problems as special  ...  [Lee, Byung Soo] (K R-K YSU; Pusan) ; Salahuddin (6-ALIG; Aligarh) General nonlinear mixed 7-type variational inequality problem. (English summary) Nonlinear Anal. Forum 8 (2003), no. 1, 11-21.  ... 

Page 1193 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
The authors use an 7-proximal mapping technique to study a class of generalized variational inequalities named strongly nonlinear quasi-variational-like inclusions, which include as special cases problems  ...  the approximating solutions of this class of generalized set-valued nonlinear quasi-variational-like inequalities by using the auxiliary principle technique.  ... 

Theory and Algorithms of Variational Inequality and Equilibrium Problems, and Their Applications

Xie-ping Ding, Nan-jing Huang, Fu-quan Xia, Qing-bang Zhang, Qamrul Hasan Ansari
2014 Abstract and Applied Analysis  
Acknowledgments The editors of this special issue would like to express their gratitude to the authors who have submitted their papers for consideration and to the expert referees who provided them with  ...  The variational inequality problem is a general problem formulation that encompasses many mathematical problems, among others, including nonlinear equations, optimization problems, complementarity problems  ...  Because of the importance and active impact of variational inequality and equilibrium problem in the nonlinear analysis and optimization, this special issue, focusing on most recent contributions, includes  ... 
doi:10.1155/2014/969303 fatcat:3kuuprppaneehnlh25jkxtcpyq

On certain classes of variational inequalities and related iterative algorithms

Muhammad Aslam Noor
1996 Journal of Applied Mathematics and Stochastic Analysis  
We also consider the auxiliary principle technique to prove the existence of a unique solution of the variational-like inequalities.  ...  This equivalence enables us to suggest and analyze a number of iterative algorithms for solving multivalued general quasi-variational inequalities.  ...  This problem is called the strongly nonlinear mixed variational-like inequality problem.  ... 
doi:10.1155/s1048953396000056 fatcat:4ytdy4cpkffaznxrzadpmeklji

Page 5279 of Mathematical Reviews Vol. , Issue 2003g [page]

2003 Mathematical Reviews  
In the present paper, the author obtains some results on nonlinear variational inequalities for upper semi-continuous H- monotone set-valued maps 7 defined on nonreflexive Banach spaces.  ...  Summary: “In this paper, we study a new class of generalized strongly nonlinear quasi-variational-like inclusions and construct a new iterative algorithm with errors for solving the generalized strongly  ... 

Page 6206 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
Carlo Bardaro (I-PERG; Perugia) 49 CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION 991:49012 49340 47H19 Ding, Xieping (PRC-SCHN; Chengdu) On general nonlinear variational inequalities in reflexive  ...  By applying a minimax inequality and the auxiliary principle, some existence and uniqueness theorems for solutions to the general nonlinear variational inequalities are proved.”  ... 

Auxiliary Principle and Iterative Algorithms for Generalized Set-Valued Strongly Nonlinear Mixed Variational-like Inequalities

Nan-jing Huang, Chuan-xian Deng
2001 Journal of Mathematical Analysis and Applications  
We prove the existence of a solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities, construct the iterative algorithm for the generalized  ...  set-valued strongly nonlinear mixed variational-like inequalities, and show the existence of a solution of the generalized set-valued strongly nonlinear mixed variational-like inequality by using the  ...  set-valued strongly nonlinear mixed variational-like inequality, and show the existence of a solution of the generalized set-valued strongly nonlinear mixed variational-like inequality by using the auxiliary  ... 
doi:10.1006/jmaa.2000.6988 fatcat:scdhvvvynvhzdclypprsxakesy

Existence of solutions for generalized nonlinear mixed variational-like inequalities in Banach spaces

Yali Zhao, Zunquan Xia, Zeqing Liu, Shin Min Kang
2006 International Journal of Mathematics and Mathematical Sciences  
We introduce and study a new class of generalized nonlinear mixed variational-like inequalities in reflexive Banach spaces.  ...  By applying Ding's technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational-like inequality, extend the auxiliary problem technique to suggest  ...  Acknowledgments The authors would like to express their thanks to the referees for helpful comments and suggestions.  ... 
doi:10.1155/ijmms/2006/36278 fatcat:7te63nvoxbcwvpczzixqipivfy

Solvability and algorithms of generalized nonlinear variational-like inequalities in reflexive Banach spaces

Haiyan Gao, Lili Wang, Liangshi Zhao
2020 Journal of Inequalities and Applications  
used to suggest an iterative algorithm for solving the generalized nonlinear variational-like inequality.  ...  This paper deals with solvability and algorithms for a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces.  ...  generalized nonlinear variational-like inequality (2.2).  ... 
doi:10.1186/s13660-020-02490-x fatcat:cjeqccvobfhfzexhepkwuivvya

Convergence and stability of three-step iterative scheme with errors for completely generalized strongly nonlinear quasivariational inequalities

Fengrong Zhang, Haiyan Gao, Zeqing Liu, Shin Min Kang
2006 Journal of Applied Mathematics and Computing  
In this paper, a new class of variational inequalities, which are called the generalized nonlinear variational-like inequalities are introduced and analyzed in Hilbert spaces.  ...  Making use of the auxiliary principle technique, some existence theorems of solutions for the generalized nonlinear variationallike inequalities are proved and an iterative algorithm to compute the approximate  ...  for the generalized nonlinear variational-like inequality.  ... 
doi:10.1007/bf02831953 fatcat:cywww46vgjfirkyyavnnvoyole

Page 1665 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
Ann. 142 (1960/1961), 305-310; MR 24 #A1120], the authors prove an existence theorem on solutions of variational-like inequality problems, which generalizes Proposition 6.2.2 of G.  ...  The generalized quasi- variational-like inequality problem is to find (u,w) € X¥ x F, ue S(u), w € T(u), such that Re(w,y(v,u)) > 0 for all v € S(u).  ... 

Selected Papers from the 10th International Conference 2009 on Nonlinear Functional Analysis and Applications

YeolJe Cho, JongKyu Kim
2010 Journal of Inequalities and Applications  
of multivalued mappings as well as extending the well-known results to more general spaces and applications in various areas of variational inequalities, complementarity problems, convex analysis, optimization  ...  During the last three decades, the problems of nonlinear analysis are a contemporary and very exhaustively studied research area and their applications can be found in functional analysis, fixed-point  ...  Agarwal, Editor-in-Chief of Journal of Inequalities and Applications for publishing Proceedings of the 10th International Conference 2009 on Nonlinear Functional Analysis and Applications as a special  ... 
doi:10.1155/2010/747463 fatcat:vpgkivln4ng4fn3uk5rk3ceaoy
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