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On weak and strong solutions of F-implicit generalized variational inequalities with applications

Lu-Chuan Zeng, Yen-Cherng Lin, Jen-Chih Yao
2006 Applied Mathematics Letters  
In this work, we study the F-implicit generalized variational inequalities in a real normed space setting. Weak solutions and strong solutions are introduced. Several existence results are derived.  ...  As an application, we study the F-implicit generalized complementarity problems and some existence results are obtained.  ...  The second and third author's research were partially supported by a grant from the National Science Council of Taiwan.  ... 
doi:10.1016/j.aml.2005.10.001 fatcat:sok6nnynrnd2xakiitytbrpwlm

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  ...  One of the most important and significant area is fixed-point theory being very rich, interesting, and extremely applicable areas of mathematics.  ...  issue of Journal of Inequalities and Applications.  ... 
doi:10.1155/2010/747463 fatcat:vpgkivln4ng4fn3uk5rk3ceaoy

Preserver Problems on Function Spaces, Operator Algebras, and Related Topics

Antonio M. Peralta, Chi-Keung Ng, Ngai-Ching Wong, Jen-Chih Yao
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 manuscripts for consideration and to the many expert referees who were involved  ...  in the reviewing process and provided us an invaluable help.  ...  Finally, hybrid and relaxed Mann iteration methods for a general system of variational inequalities with solutions being also common solutions of a countable family of variational inequalities and common  ... 
doi:10.1155/2014/723685 fatcat:m2vlipgajrgflglyndefiptc4e

On Two Iterative Methods for Mixed Monotone Variational Inequalities

Xiwen Lu, Hong-Kun Xu, Ximing Yin
2010 Fixed Point Theory and Applications  
We show that the iterative algorithm introduced in the work of Wang et al., 2001 has in general weak convergence in an infinitedimensional space, and the algorithm introduced in the paper of Noor 2001  ...  A mixed monotone variational inequality MMVI problem in a Hilbert space H is formulated to find a point u * ∈ H such that Tu where T is a monotone operator and ϕ is a proper, convex, and lower semicontinuous  ...  This paper is dedicated to Professor Wataru Takahashi on the occasion of his retirement. The second author supported in part by NSC 97-2628-M-110-003-MY3, and by DGES MTM2006-13997-C02-01.  ... 
doi:10.1155/2010/291851 fatcat:btuourg3dvd3lj3b7u36ozf2hm

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  ...  Ceng et al. analyze the strong convergence of an implicit iterative algorithm for finding a solution of the minimiza- tion problem for a convex and continuously Fréchet differentiable functional with constraints  ...  works on hemivariational inequality and multivalued variational inequality, the well-posedness and stability of equilibrium problems, the basic methods for showing the existence of solution of the equilibrium  ... 
doi:10.1155/2014/969303 fatcat:3kuuprppaneehnlh25jkxtcpyq

Fixed-Point Theory, Variational Inequalities, and Its Approximation Algorithms

Giuseppe Marino, Vittorio Colao, Yonghong Yao, Genaro López, Enrique Llorens-Fuster
2011 International Journal of Mathematics and Mathematical Sciences  
Kumam studied the weak and strong convergence of iterative methods to a solution of a variational inequality involving an α-inverse strongly monotone operator, which is also a zero of a maximal monotone  ...  F. Tan and S. S. Chang, by Y. Shehu, and by J. Zhu and S. S. Chang for solutions of generalized equilibrium problems and fixed points of nonexpansivetype mappings.  ...  Acknowledgments The editors would like to thank the authors for their interesting contributions, as well as the Staff and the Editorial Office of the journal for their valuable support.  ... 
doi:10.1155/2011/182024 fatcat:yi24zmonb5c3plzrjcwzn3jjvq

Page 1236 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
The generalized strongly nonlinear implicit variational inequality problem considered in this paper is to find an element u € B such that (g(v) —g(u), N(Tu, Au)) > f (u) — f(v) This problem contains a  ...  We also consider the auxiliary principle technique to study the existence of a solution for generalized set-valued variational inequalities and to suggest a general and novel iterative algorithm.  ... 

General viscosity implicit midpoint rule for nonexpansive mapping

Shuja Rizvi
2021 Filomat  
unique solution of the variational inequality problem.  ...  Furthermore, we provide some applications to variational inequalities, Fredholm integral equations, and nonlinear evolution equations and give a numerical example to justify the main result.  ...  Then the sequence {x n } converge strongly to a solution z of VIP (19) , which is also unique solution of variational inequality (4).  ... 
doi:10.2298/fil2101225r fatcat:wf7e2cdoozfcxjgwjfhsglxugm

Iterative Methods and Applications 2014

Giuseppe Marino, Filomena Cianciaruso, Claudio H. Morales, Luigi Muglia, D. R. Sahu
2015 Journal of Applied Mathematics  
, to the approximation of fixed points of nonlinear operators and of zeros of nonlinear operators, and to the approximation of solutions of variational inequalities.  ...  of variational inequalities problems or split feasibility problems and applications, (iv) optimization problems and their algorithmic approaches, (v) methods for the global continuation of fixed point  ...  Acknowledgments The editors would like to thank the authors for their interesting contributions, as well as the Staff and the Editorial Office of the Journal for their valuable support.  ... 
doi:10.1155/2015/207976 fatcat:iahrwjmrujd63ozjakojc2zia4

Iterative Methods and Applications

Giuseppe Marino, Filomena Cianciaruso, Luigi Muglia, Claudio H. Morales, Daya Ram Sahu
2014 Journal of Applied Mathematics  
, the approximation of fixed points of nonlinear operators, of zeros of nonlinear operators, and the approximation of solutions of variational inequalities.  ...  This special issue is focused on the latest achievements in these topics and the related applications.  ...  (ii) Iterative approximations of zeros of accretive-type operators. (iii) Iterative approximations of solutions of variational inequalities problems or split feasibility problems and applications.  ... 
doi:10.1155/2014/827064 fatcat:p43ncbk2yfbotcq2w23i4ln66q

Page 424 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
R. (5-QLD; Brisbane) Generalized variational inequalities for upper hemicontinuous and demi operators with applications to fixed point theorems in Hilbert spaces. (English summary) Serdica Math.  ...  set-valued strongly nonlinear implicit variational inequalities.  ... 

STRONG WEAK CONVERGENCE THEOREMS OF IMPLICIT HYBRID STEEPEST-DESCENT METHODS FOR VARIATIONAL INEQUALITIES

Lu-Chuan Ceng, Chinsan Lee, Jen-Chih Yao
2008 Taiwanese journal of mathematics  
We characterize the weak convergence of {u n } to the unique solution u * of the variational inequality: Applications to constrained generalized pseudoinverse are included.  ...  Assume that F is a nonlinear operator on a real Hilbert space H which is strongly monotone and Lipschitzian with constants η > 0 and κ > 0, respectively on a nonempty closed convex subset C of H.  ...  It has been widely extended to develop various algorithms for finding solutions of various classes of variational inequalities and complementarity problems; see, e.g., [21] [22] [23] .  ... 
doi:10.11650/twjm/1500602499 fatcat:y2cycpfpajddlo5acdfmul2hxe

List of contents and Author Index, Volume 19, 2006

2006 Applied Mathematics Letters  
Casasús 22 On the applicability of the Adomian method to initial value problems with discontinuities N. Ujević 32 Error inequalities for a generalized trapezoid rule X. Zhang and G.  ...  Cerone and S.S. Dragomir 283 Bounds for the Gini mean difference of an empirical distribution R. Ahmad and S.S. Irfan 294 On generalized nonlinear variational-like inequality problems C.Y.  ...  Yao 684 On weak and strong solutions of F-implicit generalized variational inequalities with applications NUMBER 8 F. Haußer and A.  ... 
doi:10.1016/s0893-9659(06)00219-9 fatcat:yaqob7cf6jenxoegamqj6icw5u

Page 2842 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
Author's introduction: “Recently much attention has been paid to the application of the finite element method for obtaining numerical solutions of variational inequalities.  ...  In this paper the author studies stochastic parabolic variational inequalities. By quite standard techniques he proves existence, uniqueness and regularity results for a class of weak solutions.  ... 

General Viscosity Implicit Midpoint Rule For Nonexpansive Mapping [article]

Shuja Haider Rizvi
2016 arXiv   pre-print
unique solution of the variational inequality problem.  ...  Furthermore, we provide some applications to variational inequalities, Fredholm integral equations, and nonlinear evolution equations.  ...  General Viscosity Implicit Midpoint Rule In this section, we prove a strong convergence theorem based on the general viscosity implicit midpoint rule for fixed point of nonexpansive mapping. operator with  ... 
arXiv:1609.06016v1 fatcat:qwwgxvyxk5e5bju2qt6kdtfqre
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