Coupled best approximation theorems for discontinuous operators in partially ordered Banach spaces

Volume 10, Issue 6, pp 2946--2956 http://dx.doi.org/10.22436/jnsa.010.06.09

Publication Date: June 25, 2017 Submission Date: April 16, 2017

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Authors

Dezhou Kong - College of Information Science and Engineering, Shandong Agricultural University, Taian, 271018, Shandong, China. - School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China. Lishan Liu - School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China. - Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia. Yonghong Wu - Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia.

Abstract

In this paper, we first discuss properties of the cone in normed product spaces. As applications, we then derive some coupled best approximation and coupled coincidence best approximation point results for discontinuous operators in partially ordered Banach spaces. Some of our results generalize those obtained in earlier work.

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Keywords

• Coupled fixed point
• best approximation
• metric projection
• discontinuous operator
• mixed monotone
• Banach space.

MSC

•  41A65
•  47H07
•  06B30

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