With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the it...With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.展开更多
Let C be a cone and consider a quasi-norm p defined on it. We study the structure of the couple （C, p） as a topological space in the case where the function p is also monotone. We characterize when the topology of a...Let C be a cone and consider a quasi-norm p defined on it. We study the structure of the couple （C, p） as a topological space in the case where the function p is also monotone. We characterize when the topology of a quasi-normed cone can be defined by means of a monotone norm. We also define and study the dual cone of a monotone normed cone and the monotone quotient of a general cone. We provide a decomposition theorem which allows us to write a cone as a direct sum of a monotone subcone that is isomorphic to the monotone quotient and other particular subcone.展开更多
In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assumi...In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.展开更多
This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mi...This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.展开更多
Mixed monotone operator is an important nonlinear operator. It exists extensively in the research of nonlinear differential and integral equations. Generally, the research of mixed monotone operators in partially orde...Mixed monotone operator is an important nonlinear operator. It exists extensively in the research of nonlinear differential and integral equations. Generally, the research of mixed monotone operators in partially ordered Banach spaces requires compactness, continuity or concavity-convexity of the operators. In this paper, without any compact and continuous assumption, we obtain some new existence and uniqueness theorems of positive fixed point of e-concave-convex mixed monotone operators in Banach spaces partially ordered by a cone, which extends the existing corresponding results.展开更多
By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x...By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.展开更多
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the...This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.展开更多
A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to s...A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to solve multicriterion clustering is put forward.The model of Ref.[3] is a special case of that proposed in this paper.展开更多
文摘With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.
基金the Spanish Ministry of Science and TechnologyFEDER under Grant BFM2003-02302
文摘Let C be a cone and consider a quasi-norm p defined on it. We study the structure of the couple （C, p） as a topological space in the case where the function p is also monotone. We characterize when the topology of a quasi-normed cone can be defined by means of a monotone norm. We also define and study the dual cone of a monotone normed cone and the monotone quotient of a general cone. We provide a decomposition theorem which allows us to write a cone as a direct sum of a monotone subcone that is isomorphic to the monotone quotient and other particular subcone.
文摘In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
基金The NSF(201701D0503-9)of Shanxi Provincethe Innovation Foundation for College Teaching Team of Shanxi University of Finance and Economics2015 Education and Teaching Reform Project(2015234)of Shanxi University of Finance and Economics
文摘In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.
文摘This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.
文摘Mixed monotone operator is an important nonlinear operator. It exists extensively in the research of nonlinear differential and integral equations. Generally, the research of mixed monotone operators in partially ordered Banach spaces requires compactness, continuity or concavity-convexity of the operators. In this paper, without any compact and continuous assumption, we obtain some new existence and uniqueness theorems of positive fixed point of e-concave-convex mixed monotone operators in Banach spaces partially ordered by a cone, which extends the existing corresponding results.
基金Supported by the Scientific Research Foundation of Henan Provincial Education Com mittee(1999110018)
文摘By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.
基金This work was supported by grants from NNSF of China(No:10271044)Scientific Research Fund of Educational Department of Anhui Province(NSF2003KJ005zd)Teaching Research Fund of Educational Department of Anhui Province(JYXM2003108).
文摘This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
文摘A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to solve multicriterion clustering is put forward.The model of Ref.[3] is a special case of that proposed in this paper.
