## Abstract and Applied Analysis

### An Application of Fixed Point Theory to a Nonlinear Differential Equation

#### Abstract

We introduce a new family of mappings on $[\mathrm{0},+\infty )$ by relaxing the nondecreasing condition on the mappings and by using the properties of this new family we present some fixed point theorems for $\alpha$-$\psi$-contractive-type mappings in the setting of complete metric spaces. By applying our obtained results, we also assure the fixed point theorems in partially ordered complete metric spaces and as an application of the main results we provide an existence theorem for a nonlinear differential equation.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 605405, 7 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425049480

Digital Object Identifier
doi:10.1155/2014/605405

Mathematical Reviews number (MathSciNet)
MR3272204

Zentralblatt MATH identifier
07022708

#### Citation

Farajzadeh, A. P.; Kaewcharoen, A.; Plubtieng, S. An Application of Fixed Point Theory to a Nonlinear Differential Equation. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 605405, 7 pages. doi:10.1155/2014/605405. https://projecteuclid.org/euclid.aaa/1425049480

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