# New Conditions of The Existence of Fixed Point in Δ- Ordered Δ Banach Algebra

## DOI:

https://doi.org/10.24297/jam.v18i.8370## Keywords:

Fixed Point, Ordered Banach Algebra, Lipschitz Mapping, Contraction Mappimg## Abstract

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.*

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*JOURNAL OF ADVANCES IN MATHEMATICS*,

*18*, 60-71. https://doi.org/10.24297/jam.v18i.8370

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