(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2020)
The main idea is to construct a new algebra and find new necessary and sufficient conditions equivalent to the existence of a fixed point. In this work, an algebra is constructed, called Δ - ordered Banach algebra, we define convergent in this new space, Topological structure on Δ ordered Banach Algebra and prove this as Hausdorff space. Also, we define new conditions as Δ- lipshtiz, Δ- contraction contraction , in this algebra construct, we prove this condition is the existence and uniqueness results of the fixed point. In this paper, we prove a common fixed point if the self-functions satisfy the new condition which is called Ф-contraction.