Contraction mapping principle with generalized altering distance function in ordered metric spaces and applications to ordinary differential equations

[摘要] The aim of this paper is to present the definition of a generalized altering distance function and to extend the results of Yan et al. (Fixed Point Theory Appl. 2012:152, 2012) and some others, and to prove a new fixed point theorem of generalized contraction mappings in a complete metric space endowed with a partial order by using generalized altering distance functions. The results of this paper can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence of a solution for a periodic boundary value problem.

[学科分类] 数学（综合）

[关键词] contraction mapping principle;partially ordered metric spaces;fixed point;generalized altering distance function;ordinary differential equations