English

Coupled fixed point theorems for $\phi$-contractive mixed monotone mappings in partially ordered metric spaces

Functional Analysis 2011-03-29 v1

Abstract

In this paper we extend the coupled fixed point theorems for mixed monotone operators F:X×XXF:X \times X \rightarrow X obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, \textit{Coupled fixed points in partially ordered metric spaces and application}, Nonlinear Anal. \textbf{74} (2011) 983-992], by weakening the involved contractive condition. An example as well an application to nonlinear Fredholm integral equations are also given in order to illustrate the effectiveness of our generalizations.

Keywords

Cite

@article{arxiv.1103.5287,
  title  = {Coupled fixed point theorems for $\phi$-contractive mixed monotone mappings in partially ordered metric spaces},
  author = {Vasile Berinde},
  journal= {arXiv preprint arXiv:1103.5287},
  year   = {2011}
}
R2 v1 2026-06-21T17:45:25.704Z