In this paper we give a strong converse inequality of type B in terms of unified K-functional Kλα （f, t2） （0 ≤λ≤ 1, 0 〈 α 〈 2） for the Meyer-Knig and Zeller-Durrmeyer type operators.
In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previou...In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previous results.展开更多
In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem c...In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.展开更多
The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solut...The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.展开更多
The main purpose of this paper is to introduce and deal with a self adaptive inertial subgradient extragradient iterative algorithm with a new and interesting stepsize rule in real Hilbert spaces.Under some proper con...The main purpose of this paper is to introduce and deal with a self adaptive inertial subgradient extragradient iterative algorithm with a new and interesting stepsize rule in real Hilbert spaces.Under some proper control conditions imposed on the coefficients and operators,we prove a new strong convergence result for solving variational inequalities with regard to pseudomonotone and Lipschitzian operators.Moreover,some numerical simulation results are given to show the rationality and validity of our algorithm.展开更多
By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing...By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.展开更多
In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are est...In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields.展开更多
In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach sp...In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces.展开更多
The approximation solvability of a generalized system for strongly g-r- pseudomonotonic nonlinear variational inequalities in Hilbert spaces is studied based on the convergence of the projection method. The results pr...The approximation solvability of a generalized system for strongly g-r- pseudomonotonic nonlinear variational inequalities in Hilbert spaces is studied based on the convergence of the projection method. The results presented in this paper improve, generalize and unify some recent results in the literature.展开更多
In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our me...In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.展开更多
A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and ex...A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained.展开更多
Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving q...Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace.In order to decrease the execution time and quicken the velocity of convergence,the proposed algorithm adopts an inertial technology.Moreover,the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant.Finally,numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms.展开更多
基金The NSF (10571040) of ChinaNSF (L2010Z02) of Hebei Normal University
文摘In this paper we give a strong converse inequality of type B in terms of unified K-functional Kλα （f, t2） （0 ≤λ≤ 1, 0 〈 α 〈 2） for the Meyer-Knig and Zeller-Durrmeyer type operators.
基金the Foundation of Higher School of Ningxia(04M33)the NSF of Ningxia University(ZR0622)
文摘In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previous results.
基金Supported by National Science Foundation of China（10571040）
文摘In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.
文摘The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.
文摘The main purpose of this paper is to introduce and deal with a self adaptive inertial subgradient extragradient iterative algorithm with a new and interesting stepsize rule in real Hilbert spaces.Under some proper control conditions imposed on the coefficients and operators,we prove a new strong convergence result for solving variational inequalities with regard to pseudomonotone and Lipschitzian operators.Moreover,some numerical simulation results are given to show the rationality and validity of our algorithm.
基金National Natural Science Foundation of China! (No. 19701O11) Foundation of "151 talent project" of Zhejiang provience.
文摘By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.
文摘In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields.
基金Supported by the National Natural Science Foundation of China
文摘In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces.
基金Supported by the Science and Technology Research Project of Chinese Ministry of Education (206123)
文摘The approximation solvability of a generalized system for strongly g-r- pseudomonotonic nonlinear variational inequalities in Hilbert spaces is studied based on the convergence of the projection method. The results presented in this paper improve, generalize and unify some recent results in the literature.
基金funded by National University ofCivil Engineering(NUCE)under grant number 15-2020/KHXD-TD。
文摘In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.
基金Research is supported by a grant of the National Scholarship Foundation of Greece (I.K.Y.)
文摘A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained.
文摘Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace.In order to decrease the execution time and quicken the velocity of convergence,the proposed algorithm adopts an inertial technology.Moreover,the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant.Finally,numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms.
