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

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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