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

Kong, Dezhou¹ ; Liu, Lishan² ; Wu, Yonghong³

¹ College of Information Science and Engineering, Shandong Agricultural University, Taian, 271018, Shandong, China;School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China
² School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China;Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia
³ Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia

Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 6, p. 2946-2956.

Résumé

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.

Détail

DOI : 10.22436/jnsa.010.06.09

Classification : 41A65, 47H07, 06B30
Keywords: Coupled fixed point, best approximation, metric projection, discontinuous operator, mixed monotone, Banach space.

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