Abstract and Applied Analysis

Positive Fixed Point of Strict Set Contraction Operators on Ordered Banach Spaces and Applications

Meiqiang Feng, Xuemei Zhang, and Weigao Ge

Full-text: Open access

Abstract

The fixed point theorem of cone expansion and compression of norm type for a strict set contraction operator is generalized by replacing the norms with a convex functional satisfying certain conditions. We then show how to apply our theorem to prove the existence of a positive solution to a second-order differential equation with integral boundary conditions in an ordered Banach space. An example is worked out to demonstrate the main results.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 439137, 13 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620752

Digital Object Identifier
doi:10.1155/2010/439137

Mathematical Reviews number (MathSciNet)
MR2674388

Zentralblatt MATH identifier
1206.47049

Citation

Feng, Meiqiang; Zhang, Xuemei; Ge, Weigao. Positive Fixed Point of Strict Set Contraction Operators on Ordered Banach Spaces and Applications. Abstr. Appl. Anal. 2010 (2010), Article ID 439137, 13 pages. doi:10.1155/2010/439137. https://projecteuclid.org/euclid.aaa/1288620752


Export citation