Abstract and Applied Analysis

On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces

Zhilong Li and Shujun Jiang

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Abstract

We presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 349305, 6 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511768

Digital Object Identifier
doi:10.1155/2013/349305

Mathematical Reviews number (MathSciNet)
MR3035229

Zentralblatt MATH identifier
1273.54064

Citation

Li, Zhilong; Jiang, Shujun. On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces. Abstr. Appl. Anal. 2013 (2013), Article ID 349305, 6 pages. doi:10.1155/2013/349305. https://projecteuclid.org/euclid.aaa/1393511768


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