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In this paper, we introduce an iterative method to approximate a common solution of a new general system of variational inequalities, a mixed equilibrium problem and a fixed point problem for a nonexpansive ... We prove that the iterative sequence converges strongly to a common solution of the three problems in the framework of Hilbert spaces. ... For the past years, many existence results and iterative algorithms for various variational inequality and variational inclusion problems have been extended and generalized in various directions using ...doi:10.12732/ijpam.v110i1.18 fatcat:2gocmbof3jazza3oib5j6risp4
We also study the convergence criteria of three-step iterative method under some mild conditions. Inertial type methods are suggested and investigated for general variational inclusions. ... We suggest and analyze three-step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent ... The authors would like to thank the referees for their valuable and constructive comments. ...doi:10.34198/ejms.9222.145164 fatcat:5vsgaqtp2jdihoupiadziaqwym
As the generation, we also consider two generalized variational inequalities, and obtain some iterative schemes and the proposed strong convergence theorems for solving these generalized variational inequalities ... set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality. ... Acknowledgements The authors would like to thank the referees for the valuable suggestions, which helped to improve this manuscript. ...doi:10.1186/1029-242x-2014-286 fatcat:5s7h66dppjcvlmf7dksoaougv4
We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. ... It is well known that the mixed variational inequalities are equivalent to the fixed point problem. ... S. ...doi:10.1155/2012/610852 fatcat:2wqj53ckfraermjzhh7eajo4cu
Journal of Computers
Solving linear variational inequality by traditional numerical iterative algorithm not only can not satisfy parallel, but also its precision has much relationship with initial values. ... Several numerical simulation results show that the coevolutionary algorithm offers an effective way to solve linear variational inequality, high convergence rate, high accuracy and robustness. ... Although there are plenty of methods proposed for solving the inequality (1), most of them rely on iterative methods. ...doi:10.4304/jcp.6.3.586-593 fatcat:qo4mzzvxprg2bmesdbcjkigw5q
In this paper, we propose a new decomposition algorithm for solving monotone variational inequality problems with linear constraints. ... At each iteration, the algorithm solves a system of nonlinear equations, which is structurally much easier to solve than variational inequality problems, the subproblems of classical decomposition methods ... Inspired by these, in this paper, we propose a new decomposition algorithm for solving variational inequality problems with S =S 1 or S =S 2 . ...doi:10.1016/j.cam.2003.08.001 fatcat:ul3tbn4pg5ewvg4nepe26yd6s4
The system of nonlinear variational inequalities (SNVI) is a useful generalization of variational inequalities. Verma (2001) suggested and analyzed an iterative method for solving SNVI. ... The author would like to thank the referee for valuable suggestions for the improvement of this paper. ... In 2005, Bnouhachem  presented a new self-adaptive method for solving general mixed variational inequalities. ...doi:10.1155/2007/23795 fatcat:bpwpxptbrjbmtkkvrpsjf4av2a
Summary: “We construct a new iterative algorithm, which includes many known algorithms as special cases, for solving variational inequalities and quasivariational inequalities for fuzzy mappings. ... 2001e:47099 47 solving variational inequalities for fuzzy mappings. ...
We use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality. ... Results proved in this paper continue to hold for these known and new classes of variational inequalities and its variant forms. ... S. M. Junaid Zaidi, Rector, COMSATS Institute of Information Technology, Pakistan, for providing the excellent research facilities. ...doi:10.1155/2012/125373 fatcat:vim3au4ppzajxohzwwk5tew754
In this paper, we consider a new system of absolute value variational inclusions. ... It is shown that variational inclusions are equivalent to the fixed point problems. ... For S = I, the identity operator, Algorithm 6.2 reduces to the following iterative method for solving variational inclusion(2.1) and appears to be a new one. Algorithm 6.3. ...doi:10.34198/ejms.8122.121153 fatcat:sxux2hggbnht3dixut5mi5ljdy
In this paper, we suggest and consider a class of new three-step approximation schemes for general variational inequalities. Our results include Ishikawa and Mann iterations as special cases. ... all n G 0 and Ý ␣ s ϱ. ␥ s 0, we obtain the perturbed Ishikawa iterative method and for n ␥ s 0 and ␤ s 0, we obtain the perturbed Mann iterative schemes for n n Ž . solving the general variational inequality ... If g s I, the identity operator, we obtain the perturbed iterative method for solving variational Ž . inequalities of type 2.2 . ...doi:10.1006/jmaa.2000.7042 fatcat:lakfjkdcrbgzfddyvv7e65dqyq
we consider and analyze some new projection-splitting algorithms for solving monotone variational inequalities by using the technique of updating the solution. ... The modified methods converge for monotone continuous operators. The new iterative method differs from the existing projection methods. ... solving variational inequalities. ...doi:10.1016/s0898-1221(00)00087-0 fatcat:y7uqerk7jvdd5cyt3afl4cabsy
This paper presents a new decomposition algorithm for solving monotone variational inequality problems with linear constraints. ... Summary: “In this paper, we develop some new implicit iteration procedures for solving a class of nonlinear set-valued mixed vari- ational inequalities. ...
This equivalence is used to suggest and analyze some iterative methods for solving the general multivalued variational in equalities in conjunction with nonexpansive mappings. ... We prove a strong convergence result for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general multivalued variational inequalities under ... Acknowledgments The authors thank the referees for useful comments and suggestions. The research of Professor M. ...doi:10.1155/2012/768272 fatcat:oarll4v7djhrvnb3zi2ajalgli
Al-Shemas, a forward backward algorithm with penalization parameters is introduced and studied for solving variational inequalities in Hilbert spaces. K. Wattanawitoon and P. ... Wangkeeree, a weakened viscosity algorithm is studied for these semigroups. For general families of mappings, iterative procedures had been examinated by S. ... 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
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