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 proximitypoint 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.