Fixed point theorems for convex contractions on cone 2-metric space over Banach algebra

Abstract

In 2007, B.Singh, S Jain and P Bhagat introduced cone 2-metric space and proved some fixed point theorems of certain contractive mappings while Tao Wang, Jiangdong Yin, and Qi Yan introduced cone 2-metric spaces over Banach algebra and established some existence and uniqueness theorems of fixed points for some contractive mappings. In this paper, we extended some results of Istra{\c{t}}escu's convex contractions to cone 2-metric space over Banach algebra and presented two fixed point theorems. Examples are given showing the significance of our results.