A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a...A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the existence of solutions and convergence of approximate solutions for general multivalued mixed implicit quasi-variational inequalities are proved. Moreover, the new convergerce criteria for the algorithm were provided. Therefore, the results give an affirmative answer to the open question raised by M. A . Noor, and extend and improve the earlier and recent results for various variational inequalities and complementarity problems including the corresponding results for mixed variational inequalities, mixed quasi-variational inequalities and quasi-complementarity problems involving the single-valued and set- valued mappings in the recent literature .展开更多
By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative a...By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.展开更多
In this paper, by using the auxiliary technique of variational inequalities, the existence and iterative algorithm; of solutions for a class of generalized mixed quasi-variational inequalities are studied. Our results...In this paper, by using the auxiliary technique of variational inequalities, the existence and iterative algorithm; of solutions for a class of generalized mixed quasi-variational inequalities are studied. Our results answer the open problems mentioned by Noor, improve and generalize some recent known results.展开更多
The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation...The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.展开更多
The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symm...The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.展开更多
A quasi-variational inequality is proved in paracompact setting which generalizes the results of Zhou Chen andAubin. As applications, two existence theorems on the solutions of optimization problems and social equilib...A quasi-variational inequality is proved in paracompact setting which generalizes the results of Zhou Chen andAubin. As applications, two existence theorems on the solutions of optimization problems and social equilibria ofmetagames are showed which improve and extend the recent results of Kaczynski-Zeidan and Aubin.展开更多
We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping...We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.展开更多
An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for...An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.展开更多
Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curv...Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curvature images being a special case. The properties and Lp analogs of the affne isoperimetric inequality are established for Lp-mixed curvature images.展开更多
In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solu...In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.展开更多
In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski typ...In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski type inequality and Aleksandrov-Fenchel inequality for the polars of mixed complex projection bodies.展开更多
The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due...The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.展开更多
A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven tha...A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.展开更多
In this paper, we investigate the translative containment measure for a convex domain Ki to contain, or to be contained in the homothetic copy of another convex domain tKj(t ≥ 0). Via the formulas of translative Blas...In this paper, we investigate the translative containment measure for a convex domain Ki to contain, or to be contained in the homothetic copy of another convex domain tKj(t ≥ 0). Via the formulas of translative Blaschke and Poincaré in integral formula, we obtain a Bonnesen-style symmetric mixed isohomothetic inequality. The Bonnesen-style symmetric mixed isohomothetic inequality obtained is known as Bonnesen-style inequality if one of the domains is a disc. As a direct consequence, we attain an inequality which strengthen the result proved by Bonnesen, Blaschké and Flanders. Furthermore, by the containment measure and Blaschke's rolling theorem, we obtain the reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These inequalities are the analogues of the known Bottema's result in 1933.展开更多
Tarnavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequslity was derived in this paper. As its applications, some separations of other inequalities were given.
In this paper, with the use of the friction problem in elasticity as the background, the existence and uniqueness for the solution of the nonlinear, indifferentiable mixed variational inequality are discussed. Its cor...In this paper, with the use of the friction problem in elasticity as the background, the existence and uniqueness for the solution of the nonlinear, indifferentiable mixed variational inequality are discussed. Its corresponding boundary variational inequality and the existence and uniqueness, of solution are given. This provides the theoretical basis for using boundary element method to solve the mixed variational inequality.展开更多
In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the ...In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.展开更多
基金the Teaching and Research Award Fund for Qustanding Young Teachers in Higher Education Institutions of MOE, PRC the Special Funds for Major Specialities of Shanghai Education Committee+1 种基金the Department Fund of ScienceTechnology in Shanghai Higher Educ
文摘A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the existence of solutions and convergence of approximate solutions for general multivalued mixed implicit quasi-variational inequalities are proved. Moreover, the new convergerce criteria for the algorithm were provided. Therefore, the results give an affirmative answer to the open question raised by M. A . Noor, and extend and improve the earlier and recent results for various variational inequalities and complementarity problems including the corresponding results for mixed variational inequalities, mixed quasi-variational inequalities and quasi-complementarity problems involving the single-valued and set- valued mappings in the recent literature .
文摘By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.
基金the Natural Science Foundation of Sichuan Education Com mittee
文摘In this paper, by using the auxiliary technique of variational inequalities, the existence and iterative algorithm; of solutions for a class of generalized mixed quasi-variational inequalities are studied. Our results answer the open problems mentioned by Noor, improve and generalize some recent known results.
基金received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement(823731-CONMECH)supported by the National Science Center of Poland under Maestro Project(UMO-2012/06/A/ST1/00262)+3 种基金National Science Center of Poland under Preludium Project(2017/25/N/ST1/00611)supported by the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland(3792/GGPJ/H2020/2017/0)Qinzhou University Project(2018KYQD06)National Natural Sciences Foundation of Guangxi(2018JJA110006)
文摘The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.
文摘The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.
文摘A quasi-variational inequality is proved in paracompact setting which generalizes the results of Zhou Chen andAubin. As applications, two existence theorems on the solutions of optimization problems and social equilibria ofmetagames are showed which improve and extend the recent results of Kaczynski-Zeidan and Aubin.
基金supported by the Scientific Research Foundation of Sichuan Normal University(20151602)National Natural Science Foundation of China(10671135,61179033)and the Key Project of Chinese Ministry of Education(212147)
文摘We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.
基金Project supported by the National Natural Science Foundation of China (No.10472061)
文摘An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.
基金Supported by Innovation Program of Shanghai Municipal Education Commission (10YZ160)Science and Technology Commission Foundation of Shanghai (071605123)Science Foundation for the Excellent Youth Scholars of Shanghai
文摘Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curvature images being a special case. The properties and Lp analogs of the affne isoperimetric inequality are established for Lp-mixed curvature images.
文摘In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.
文摘In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski type inequality and Aleksandrov-Fenchel inequality for the polars of mixed complex projection bodies.
基金This research was supported by MOEC (20060284001)NSFC (70371019 and 10571083)supported partly by NSFC 70571034
文摘The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.
基金supported by the Key Program of National Natural Science Foundation of China(No.70831005)the National Natural Science Foundation of China(No.10671135)the Fundamental Research Funds for the Central Universities(No.2009SCU11096)
文摘A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.
基金supported in part by the National Natural Science Foundation of China(11801048)the Natural Science Foundation Project of CSTC(cstc2017jcyjAX0022)Innovation Support Program for Chongqing overseas Returnees(cx2018034)
文摘In this paper, we investigate the translative containment measure for a convex domain Ki to contain, or to be contained in the homothetic copy of another convex domain tKj(t ≥ 0). Via the formulas of translative Blaschke and Poincaré in integral formula, we obtain a Bonnesen-style symmetric mixed isohomothetic inequality. The Bonnesen-style symmetric mixed isohomothetic inequality obtained is known as Bonnesen-style inequality if one of the domains is a disc. As a direct consequence, we attain an inequality which strengthen the result proved by Bonnesen, Blaschké and Flanders. Furthermore, by the containment measure and Blaschke's rolling theorem, we obtain the reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These inequalities are the analogues of the known Bottema's result in 1933.
基金Project supported by National Natural Science Foundation of China （Grant No. 10271071）
文摘Tarnavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequslity was derived in this paper. As its applications, some separations of other inequalities were given.
文摘In this paper, with the use of the friction problem in elasticity as the background, the existence and uniqueness for the solution of the nonlinear, indifferentiable mixed variational inequality are discussed. Its corresponding boundary variational inequality and the existence and uniqueness, of solution are given. This provides the theoretical basis for using boundary element method to solve the mixed variational inequality.
基金The first author was supported by the Guangxi Natural Science Foundation of China(Grant No.2021GXNSFFA196004)National Natural Science Foundation of China(Grant No.12001478)+4 种基金Horizon 2020 of the European Union(Grant No.823731 CONMECH)National Science Center of Poland(Grant No.2017/25/N/ST1/00611)The second author was supported by National Science Foundation of USA(Grant No.DMS 1720067)The third author was supported by the National Science Center of Poland(Grant No.2021/41/B/ST1/01636)the Ministry of Science and Higher Education of Poland(Grant Nos.4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019)。
文摘In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.
