COMMON BEST PROXIMITY POINT THEOREMS ON CONE B-METRIC SPACES OVER BANACH ALGEBRAS

Year 2017, Volume: 30 Issue: 2, 159 - 172, 19.06.2017

Seyed Masoud Aghayan Ahmad Zireh Ali Ebadian

Abstract

In this paper, we obtain the existence of some common best proximity
point theorems for generalized Lipschitz contractive mappings on cone b-metric space over Banach algebra without assumption of normality. Our results generalize the corresponding result by Xu and Radenovic (Fixed Point Theory and Appl. 2014, 2014:102) and by Huang and Radenovic ( J. Computational Anal. and Appl. 2016, 20(3)). Further, we give an example to illustrate that our works are never equivalent with the counterparts in the literature.

Keywords

Common best proximity point theorems, Cone metric spaces over Banach algebras, Generalized Lipschitz mappings, c-sequence.

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