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

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 insert ignore into journalissuearticles values(Fixed Point Theory and Appl. 2014, 2014:102); and by Huang and Radenovic insert ignore into journalissuearticles values( J. Computational Anal. and Appl. 2016, 20insert ignore into journalissuearticles values(3););. Further, we give an example to illustrate that our works are never equivalent with the counterparts in the literature.