Let A, B be two unital C^＊-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h ： A →B which satisfies h（2^nuy） = h（2^nu）h（y） for all u ∈ U（A）, all y ∈ A, and a...Let A, B be two unital C^＊-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h ： A →B which satisfies h（2^nuy） = h（2^nu）h（y） for all u ∈ U（A）, all y ∈ A, and all n = 0,1,2,..., is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of ,-homomorphisms on unital C^＊-algebras.展开更多
Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-...Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-algebras） for the generalized Jensen–type functional equationwhere r is a fixed positive real number in （1, ∞）.展开更多
We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into ...We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .展开更多
Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is con...Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.展开更多
In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） i...In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.展开更多
In this paper, we investigate the general solution and the stability of a cubic functional equation f（x ＋ ny） ＋ f（x - ny） ＋ f（nx） = n^2 f（x ＋ y） ＋ n^2 f（x - y）＋ （n^3 - 2n^2 ＋ 2）f（x）,where n ≥ 2 i...In this paper, we investigate the general solution and the stability of a cubic functional equation f（x ＋ ny） ＋ f（x - ny） ＋ f（nx） = n^2 f（x ＋ y） ＋ n^2 f（x - y）＋ （n^3 - 2n^2 ＋ 2）f（x）,where n ≥ 2 is an integer. Furthermore, we prove the stability by the fixed point method.展开更多
Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the fin...Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.展开更多
The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The prox...The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximM ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to soNe the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O（1/k） in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.展开更多
文摘Let A, B be two unital C^＊-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h ： A →B which satisfies h（2^nuy） = h（2^nu）h（y） for all u ∈ U（A）, all y ∈ A, and all n = 0,1,2,..., is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of ,-homomorphisms on unital C^＊-algebras.
文摘Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-algebras） for the generalized Jensen–type functional equationwhere r is a fixed positive real number in （1, ∞）.
文摘We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .
文摘Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.
文摘In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.
文摘In this paper, we investigate the general solution and the stability of a cubic functional equation f（x ＋ ny） ＋ f（x - ny） ＋ f（nx） = n^2 f（x ＋ y） ＋ n^2 f（x - y）＋ （n^3 - 2n^2 ＋ 2）f（x）,where n ≥ 2 is an integer. Furthermore, we prove the stability by the fixed point method.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11301521, 11771467, 11071041）, the Natural Science Foundation of Fujian Province （Nos. 2016J01005, 2015J01578）, and the National Post- doctoral Program for Innovative Talents （No. BX201700234）.
文摘Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.
基金supported by the National Natural Science Foundation of China(11571074,61170308)the Natural Science Foundation of Fujian Province(2015J01010)the Major Science Foundation of Fujian Provincial Department of Education(JA14037)
文摘The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximM ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to soNe the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O（1/k） in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.
