A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations

By Fangfang Yan, Yongfu Su, Qiansheng Feng. Fixed Point Theory and Applications, 2012

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The aim of this paper is to extend the results of Harjani and Sadarangani and some other authors and to prove a new fixed point theorem of a contraction mapping in a complete metric space endowed with a partial order by using altering distance functions. Our theorem 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4b1e1dca9d4235957c0bbc99e8dc36bf6e457896