论文信息 - Fixed point theorems in partially ordered metric spaces and applications

Fixed point theorems in partially ordered metric spaces and applications

Abstract We prove a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order, using a weak contractivity type of assumption. Besides including several recent developments, our theorem can be used to investigate a large class of problems. As an application, we discuss the existence and uniqueness of solution for a periodic boundary value problem.

V. Lakshmikantham | T. Gnana Bhaskar | V. Lakshmikantham | T. Bhaskar

[1] Juan J. Nieto,et al. Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations , 2007 .

[2] A. Ran,et al. A fixed point theorem in partially ordered sets and some applications to matrix equations , 2003 .

[3] V. Lakshmikantham,et al. Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations , 2003 .

[4] V. Lakshmikantham,et al. Theory of Fuzzy Differential Equations and Inclusions , 2003 .

[5] V. Lakshmikantham,et al. Theory of Set Differential Equations in Metric Spaces , 2005 .

[6] W. Ames,et al. Nonlinear problems in abstract cones , 1988 .

[7] V. Lakshmikantham,et al. Monotone iterative techniques for nonlinear differential equations , 1985 .

[8] V. Lakshmikantham,et al. Nonlinear variation of parameters formula for set differential equations in a metric space , 2005 .

[9] Juan J. Nieto,et al. Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations , 2005, Order.

[10] V. Lakshmikantham,et al. Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations , 1994 .