By using the theory of the cone and partial ordering. It is studied that theexistence 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(...By using the theory of the cone and partial ordering. It is studied that theexistence 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 Aand B can be decomposed A = A1+A2,B = B1+B2, A1 and B1 are mixed monotone, A2and B2 are anti-mixed monotone. The results preeented here improve and generalize somecorresponding results of mixed monotone operator equations.展开更多
By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this pape...By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.展开更多
In this paper, the existence and uniqueness of solution systems for some binary nonlinear operator equations are discussed by using cone and partially order theory and monotone iteration theory, and the iterative sequ...In this paper, the existence and uniqueness of solution systems for some binary nonlinear operator equations are discussed by using cone and partially order theory and monotone iteration theory, and the iterative sequences which converge to solution of operator equations and error estimates for iterative sequences are also given. Some corresponding results are improved and generalized. Finally, the applications of our results are given.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
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, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative...In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.展开更多
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 theexistence 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 Aand B can be decomposed A = A1+A2,B = B1+B2, A1 and B1 are mixed monotone, A2and B2 are anti-mixed monotone. The results preeented here improve and generalize somecorresponding results of mixed monotone operator equations.
文摘By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.
文摘In this paper, the existence and uniqueness of solution systems for some binary nonlinear operator equations are discussed by using cone and partially order theory and monotone iteration theory, and the iterative sequences which converge to solution of operator equations and error estimates for iterative sequences are also given. Some corresponding results are improved and generalized. Finally, the applications of our results are given.
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.
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.
文摘In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.
