Several New Types of Fixed Point Theorems and Their Applications to Two-Point Ordinary Differential Equations

Congjun Zhang, Jinlu Li, Yan Zhang, Xiaoliang Feng

Department of Mathematics, Nanjing University, Nanjing, Jiangsu, People’s Republic of China.
Department of Mathematics, Shawnee State University, Portsmouth, Ohio, USA.
School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, People’s Republic of China.

DOI: 10.4236/am.2012.310163                

Abstract

The present paper is mainly concerned with several new types of fixed point theorems in different spaces such as cone metric spaces and fuzzy metric spaces. By using these obtained fixed point theorems, we then prove the existence and uniqueness of the solutions to two classes of two-point ordinary differential equation problems.

Keywords

Expansive Mapping; Cone Metric Space; Fuzzy Metric Space; Two-Point Ordinary Differential Equations

Conflicts of Interest

The authors declare no conflicts of interest.

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