Hybrid projection method for generalized mixed equilibrium problems,variational inequality problems,and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.     

Hybrid projection method for generalized mixed equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.     

Theory of pressure swirl atomisation and study on the characteristic of droplet size in atomisation

Based on the observation of the working condition in pressure swirl atomisationexperiments,this article tries to suggest a model of the mechanism of pressure swirlatomisation—the atomisation theory of pressure swirl spray of conical film.Under somebasic assumptions,the formula for the characteristic of droplet size of pressure swirlatomisation is derived:The above theory agrees basically with the actual working conditions in atomisation,andgives the latter a compratively good interpretation.In this article,theoretical calculations are worked out for the characteristic ofatomised droplet size of some Oil atomising nozzles used in power plants in our country(thePeople＇s Republic of China)and are compared with actual test data.The results show thatthe theory is of some value to preactice,and it is recommended to those concerned forreference.     

On a class of generalized nonlinear implicit quasivariational inclusions

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Generalized mixed equilibrium problem in Banach spaces

This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.     

Viscosity approximation with weak contractions for fixed point problem,equilibrium problem,and variational inequality problem

This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.（Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715（2009））,Plubtieng and Punpaeng（Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469（2007））,Colao et al.（Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352（2008））,Yao et al.（Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363（2007）DOI 10.1155/2007/64363）,and others.     

On the existence and uniqueness of solutions for a class of variational inequalities with applications to the signorini problem in mechanics

In this paper,we introduce a new unified and general class of variational inequalities,and show some existence and uniqueness results of solutions for this kind of variationalinequalities.As an application,we utilize the results presented in this paper to study theSignorini problem in mechanics.     

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.     

Optimal control of parabolic variational inequalities with state constraint

1　IntroductionandProblemWeshallstudytheoptimalcontrolproblemsgovernedbynonlinearparabolicvariationalinequalitiesoftheformy′+Ay +β(y) ∈Bu+f(a.e .(x,t)∈Q =Ω× [0 ,t]) ,y(0 ) =y0 , ( )withthestateconstraintF(y) S ,andthecostfunctionalI(y,u) .Whereβisadiscontinuous,nonlinearandnonmonotonemulti_valuedmapping .Theoptimalcontrolproblemsofthedifferentialsystemshavebeenstudiedforalongtime.Manyscholars,suchasJ.L .Lions ,V .Barbu ,D .Tiba,andF .Mignotetal.,haveresearchedtheoptimalcontrolpr…     

Existence and algorithm of solutions for general multivalued mixed implicit quasi-variational inequalities

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 e     

On uniform convergence of linear operators on the probabilistic normed space

In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic normed space, and the notion of probabilistic distance between the operators, which describes the above convergence completely. In terms of these notions, we obtained the essential features of the continuity of operators, and of the uniform convergence of operator sequences, and we also obtained the closure of continuity and complete continuity under the operation of the limit of uniform convergence.     

Uniform strength design of beams with non-zero minimum flexural rigidity under multiple loadings

The analytical method for uniform strength design (U.S.D.) of statically indeterminate beams is extended to deal with a preassigned constraint of non-zero minimum flexural rigidity and multiple load cases. And a numerical method of finding the U.S.D. is presented. Therefore we have a uniform procedure of solution of U.S.D. to beams with arbitrary cross-sectional shape and acted upon by several loadings and subjected to the constraint of minimum flexural rigidity.     

On CFL evolution strategies for implicit upwind methods in linearized Euler equations

In implicit upwind methods for the solution of linearized Euler equations, one of the key issues is to balance large time steps, leading to a fast convergence behavior, and small time steps, needed to sufficiently resolve relevant flow features. A time step is determined by choosing a Courant–Friedrichs–Levy (CFL) number in every iteration. A novel CFL evolution strategy is introduced and compared with two existing strategies. Numerical experiments using the adaptive multiscale finite volume solver QUADFLOW demonstrate that all three CFL evolution strategies have their advantages and disadvantages. A fourth strategy aiming at reducing the residual as much as possible in every time step is also examined. Using automatic differentiation, a sensitivity analysis investigating the influence of the CFL number on the residual is carried out confirming that, today, CFL control is still a difficult and open problem. Copyright © 2008 John Wiley & Sons, Ltd.     

The perturbation-iterative method applied to the problems of the large deflection of the elastic circular thin plates

In this paper, we present a perturbation-iterative method for solving certain boundary value problems encountered in the nonlinear theory of elastic circular thin plates. At the same time, with this method, we strictly prove the convergence of the solutions for the large deflection equations of circular plates subjected to certain distributed loads.     

Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium

A new system of generalized mixed implicit equilibrium problems(SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces.First,an auxiliary mixed equilibrium problem(AMEP) is introduced.The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions.Next,by using the solution mapping of the AMEP,a system of generalized equation problems(SGEP) is considered,and its equivalence with the SGMIEP is shown.By using the SGEP,a new iterative algorithm for solving the SGMIEP is proposed and analyzed.The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions.These results are new,which unify and generalize some recent results in this field.     

Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems

We derive and investigate point implicit Runge–Kutta methods to significantly improve the convergence rate to approximate steady‐state solutions of inviscid flows. It turns out that the point implicit Runge–Kutta can be interpreted as a preconditioned explicit Runge–Kutta method, where the preconditioner arises naturally as local derivative of the residual function. Moreover, many preconditioners suggested in the literature so far are identified as special case of our general ansatz. Conditions will be formulated such that explicit Runge–Kutta methods with local time stepping are equivalent to point implicit methods. In numerical examples, we will demonstrate the improved convergence rates. Copyright © 2011 John Wiley & Sons, Ltd.     

Strong convergence theorem for a generalized equilibrium problem and a <Emphasis Type="Italic">k</Emphasis>-strict pseudocontraction in Hilbert spaces

The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontractive mapping in the Hilbert space. The presented results extend and improve the corresponding results reported in the lit-erature.     

On the variational principles in linear elastodynamics

A new approach is proposed for the systematic derivation of varïous variational principles in linear elastodynamics. Based on an important integral relation in terms of convolutions given by the authors, the new approach can be used to derive the complementary functionals for the five-field, four-field, three-field, two-field and one-field variational principles more simply and directly. Furthermore, with this approach, it is possible not only to derive the variational principles given by Herrera and Bielak, Oden and Reddy, but also to develop new more general variational principles. And the intrinsic relationship among various principles can be explained clearly.     

Behavior of solution set for bilevel generalized mixed equilibrium problems in topological vector spaces

A new bilevel generalized mixed equilibrium problem （BGMEF） is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field.     

On the Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings in Banach spaces

The purpose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results by Chang, Ding, Hassouni, Kazmi, Siddiqi, Zeng et al. Foundation item: the National Natural Science Foundation of China (19771058)