In this paper, the author establishs general open mapping theorems for continuous, weakly continuous, closed and weakly singular linear maps respectively. From these general theorems, he deduces a lot of specific open...In this paper, the author establishs general open mapping theorems for continuous, weakly continuous, closed and weakly singular linear maps respectively. From these general theorems, he deduces a lot of specific open mapping theorems, which include some well-known theorems and some new interesting results. Particularly the author gives the extensions of Husain's open mapping theorem and Adasch's open mapping theorem.展开更多
The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the co...The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.展开更多
In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence th...In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence theorems.matching theorems and vector valued minimax inequalities which generalize slightly thecorresponding results in[1,2,4,5,6,7].展开更多
Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed c...Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:for all x,y in K,where then T has a unique fixed point in K.展开更多
The purpose of this paper is to study the section theorems,coincidence theorems and intersection theorems on H-spaces.As a way of application,we use these results to study the existence problems of solutions for minim...The purpose of this paper is to study the section theorems,coincidence theorems and intersection theorems on H-spaces.As a way of application,we use these results to study the existence problems of solutions for minimax inequalities and variational inequalities.The results presented in this paper improve and extend the corresponding results in[1,3,5,6,8,9,12,14,15,17]展开更多
For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and th...For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.展开更多
In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigro...In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigroup don't increase under the A-smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of the spectrum of generator and semgroup.展开更多
In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H(B^n)...In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H(B^n) satisfying ||f||0 = 1 and det f'(0) = α ∈ (0, 1], where||f||0 = sup{(1 - |z|^2 )n+1/2n det(f'(z))[1/n : z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f(0). When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.展开更多
In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Legg...In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.展开更多
In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations be...In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations between approximate solutions and solutions are studied. In the end ,the existence theorem of solutions to differential inclusions is obtained.展开更多
Some new continuous selection theorems are first proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings de...Some new continuous selection theorems are first proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product space of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in recent literature.展开更多
We first study the Grassmannian manifoldG n (Rn+p)as a submanifold in Euclidean space Λ n (R n+p). Then we give a local expression for each map from Riemannian manifoldM toG n (R n+p) ?Λ n (R n+p), and use the local...We first study the Grassmannian manifoldG n (Rn+p)as a submanifold in Euclidean space Λ n (R n+p). Then we give a local expression for each map from Riemannian manifoldM toG n (R n+p) ?Λ n (R n+p), and use the local expression to establish a formula which is satisfied by any harmonic map fromM toG n (R n+p). As a consequence of this formula we get a rigidity theorem.展开更多
文摘In this paper, the author establishs general open mapping theorems for continuous, weakly continuous, closed and weakly singular linear maps respectively. From these general theorems, he deduces a lot of specific open mapping theorems, which include some well-known theorems and some new interesting results. Particularly the author gives the extensions of Husain's open mapping theorem and Adasch's open mapping theorem.
文摘The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.
文摘In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence theorems.matching theorems and vector valued minimax inequalities which generalize slightly thecorresponding results in[1,2,4,5,6,7].
文摘Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:for all x,y in K,where then T has a unique fixed point in K.
基金Project supported by the National Natural Science Foundation of China
文摘The purpose of this paper is to study the section theorems,coincidence theorems and intersection theorems on H-spaces.As a way of application,we use these results to study the existence problems of solutions for minimax inequalities and variational inequalities.The results presented in this paper improve and extend the corresponding results in[1,3,5,6,8,9,12,14,15,17]
基金The NSF (Q1107107) of Jiangsu Educational Commission.
文摘For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.
文摘In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigroup don't increase under the A-smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of the spectrum of generator and semgroup.
基金supported by NNSF of China (Grant No.10826083)supported by NNSF of China (Grant No.10571164)+1 种基金NSF of Zhejiang province (Grant No.D7080080)SRFDP of Higher Education (Grant No.20050358052)
文摘In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H(B^n) satisfying ||f||0 = 1 and det f'(0) = α ∈ (0, 1], where||f||0 = sup{(1 - |z|^2 )n+1/2n det(f'(z))[1/n : z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f(0). When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.
文摘In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.
文摘In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations between approximate solutions and solutions are studied. In the end ,the existence theorem of solutions to differential inclusions is obtained.
基金This project is supported by the NSF of Sichuan Education Department of China(2003A081)and SZD0406
文摘Some new continuous selection theorems are first proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product space of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in recent literature.
文摘We first study the Grassmannian manifoldG n (Rn+p)as a submanifold in Euclidean space Λ n (R n+p). Then we give a local expression for each map from Riemannian manifoldM toG n (R n+p) ?Λ n (R n+p), and use the local expression to establish a formula which is satisfied by any harmonic map fromM toG n (R n+p). As a consequence of this formula we get a rigidity theorem.