In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly sm...In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.展开更多
A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence o...A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.展开更多
In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real...In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.展开更多
In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde...In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0¥ ( hk - 1 ) < + ¥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.展开更多
In this article,we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-c...In this article,we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-contraction mapping and the set of zeros of monotone inclusion problems on Hadamard manifolds.As applications,we use our results to study the minimization problems and equilibrium problems in Hadamard manifolds.展开更多
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 poin...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.展开更多
By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are st...By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are studied.The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers.Especially,some new techniques are used in this paper.展开更多
By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978),the abstract result on the existence of a solution u ∈ L^p (Ω) to nonlinear equations involving p...By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978),the abstract result on the existence of a solution u ∈ L^p (Ω) to nonlinear equations involving p-Laplacian operator △p, where 2N/N+1〈p〈+∞ and N (≥ 1 ) denotes the dimension of R^N,is studied. The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen's previous papers. To obtain the result ,some new techniques are used.展开更多
The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly mono...The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich(Ekonomika i Matematicheskie Metody,1976,12(4):747-756),but also extend and replenish the corresponding results obtained by Iiduka and Takahashi(Nonlinear Anal TMA,2005,61(3):341-350),Takahashi and Toyoda(J Optim Theory Appl,2003, 118(2):417-428),Nadezhkina and Takahashi(J Optim Theory Appl,2006,128(1):191- 201),and Zeng and Yao(Taiwan Residents Journal of Mathematics,2006,10(5):1293-1303).展开更多
In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized non...In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is Proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given, As special cases, some known results in this field are also discussed.展开更多
The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating ...The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results.展开更多
One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a(au/at), studied in this paper, where the item au/at which makes it more general. The...One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a(au/at), studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2(O, T; L2 (Ω)) is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.展开更多
This paper deals with optimal control problem of parabolic differential equation with two point boundary conditions tin the time variable). The results here extend those in [3] on optimal control of the heat equations...This paper deals with optimal control problem of parabolic differential equation with two point boundary conditions tin the time variable). The results here extend those in [3] on optimal control of the heat equations. Moreover, the technique used in this paper is based on some smooth approximations of 'tangent cones' in the sense of Clarke and some maximal monotone operators.展开更多
This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.
In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(α(x, Du)+F(u)) ∈ f in fΩ, where f ∈ L1 (Ω). A vector field a(.,....In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(α(x, Du)+F(u)) ∈ f in fΩ, where f ∈ L1 (Ω). A vector field a(.,.) is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.展开更多
In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McK ean-Vlasov equation. Moreover, under continuous and linear growth assumptions, ...In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McK ean-Vlasov equation. Moreover, under continuous and linear growth assumptions, we also obtain the existence of weak solutions.展开更多
The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces.
This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusionβ(u)+A(u)+g(x,u,Du)■f,where A is a Leray-Lions operator fr...This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusionβ(u)+A(u)+g(x,u,Du)■f,where A is a Leray-Lions operator from W^(1,p)_(0)(Ω)into its dual,βmaximal monotone mapping such that 0∈β(0),while g(x,s,ξ)is a nonlinear term which has a growth condition with respect toξand no growth with respect to s but it satisfies a signcondition on s.The right hand side f is assumed to belong to L^(1)(Ω).展开更多
Using perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present the abstract results on the existence of solutions of one kind nonlinear Neumann boundary value problems r...Using perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present the abstract results on the existence of solutions of one kind nonlinear Neumann boundary value problems related to p-Laplacian operator. The equation discussed in this paper and the method used here extend and complement some of the previous work.展开更多
基金the National Natural Science Foundation of China (10771050)
文摘In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.
基金Supported by the National Natural Science Foundation of China
文摘A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.
基金Supported by the National Natural Science Foundation of China(10771050)the Natural Science Foun-dation of Hebei Province(A2010001482)
文摘In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.
基金Supported both by the Teaching and Research Award Fund for Outstanding Young Teachers inHigher Educational Institutions of MOEChinaand by the Dawn Program Fund in Shanghai
文摘In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0¥ ( hk - 1 ) < + ¥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.
基金This study was supported by the Natural Science Foundation of China Medical University,TaiwanThis work was also supported by Scientific Research Fund of SiChuan Provincial Education Department(14ZA0272).
文摘In this article,we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-contraction mapping and the set of zeros of monotone inclusion problems on Hadamard manifolds.As applications,we use our results to study the minimization problems and equilibrium problems in Hadamard manifolds.
基金supported by the Natural Science Foundation of Yibin University (No. 2009Z003)
文摘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.
文摘By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are studied.The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers.Especially,some new techniques are used in this paper.
文摘By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978),the abstract result on the existence of a solution u ∈ L^p (Ω) to nonlinear equations involving p-Laplacian operator △p, where 2N/N+1〈p〈+∞ and N (≥ 1 ) denotes the dimension of R^N,is studied. The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen's previous papers. To obtain the result ,some new techniques are used.
基金the Natural Science Foundation of Yibin University of China(No.2007-Z003)
文摘The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich(Ekonomika i Matematicheskie Metody,1976,12(4):747-756),but also extend and replenish the corresponding results obtained by Iiduka and Takahashi(Nonlinear Anal TMA,2005,61(3):341-350),Takahashi and Toyoda(J Optim Theory Appl,2003, 118(2):417-428),Nadezhkina and Takahashi(J Optim Theory Appl,2006,128(1):191- 201),and Zeng and Yao(Taiwan Residents Journal of Mathematics,2006,10(5):1293-1303).
文摘In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is Proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given, As special cases, some known results in this field are also discussed.
基金supported by the Natural Science Foundation of Yibin University (No.2009-Z003)
文摘The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results.
基金supported by the National Natural Science Foundation of China(11071053)Natural Science Foundation of Hebei Province(A2014207010)+1 种基金Key Project of Science and Research of Hebei Educational Department(ZD2016024)Key Project of Science and Research of Hebei University of Economics and Business(2015KYZ03)
文摘One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a(au/at), studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2(O, T; L2 (Ω)) is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.
文摘This paper deals with optimal control problem of parabolic differential equation with two point boundary conditions tin the time variable). The results here extend those in [3] on optimal control of the heat equations. Moreover, the technique used in this paper is based on some smooth approximations of 'tangent cones' in the sense of Clarke and some maximal monotone operators.
基金supported by NSFs of China(11471340 and 11461028)
文摘This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.
文摘In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(α(x, Du)+F(u)) ∈ f in fΩ, where f ∈ L1 (Ω). A vector field a(.,.) is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.
基金supported by the National Natural Science Foundation of China(11271294)
文摘In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McK ean-Vlasov equation. Moreover, under continuous and linear growth assumptions, we also obtain the existence of weak solutions.
基金Supported by the Vietnamese Natural Foundation for Science and Technology Development 2009
文摘The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces.
文摘This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusionβ(u)+A(u)+g(x,u,Du)■f,where A is a Leray-Lions operator from W^(1,p)_(0)(Ω)into its dual,βmaximal monotone mapping such that 0∈β(0),while g(x,s,ξ)is a nonlinear term which has a growth condition with respect toξand no growth with respect to s but it satisfies a signcondition on s.The right hand side f is assumed to belong to L^(1)(Ω).
基金Supported by the National Natural Science Foundation of China (No. 11071053)the Natural Science Foundation of Hebei Province (No.A2010001482)the project of Science and Research of Hebei Education Department (the second round in 2010)
基金Supported by the National Natural Science Foundation of China (Grant No.10771050)the Project of Science and Research of Hebei Education Department (Grant No.2009115)
文摘Using perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present the abstract results on the existence of solutions of one kind nonlinear Neumann boundary value problems related to p-Laplacian operator. The equation discussed in this paper and the method used here extend and complement some of the previous work.