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

## Authors

• Boushra Hussein University of Al-Qadisiyah/College of Education

## 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.

## Author Biography

### Boushra Hussein, University of Al-Qadisiyah/College of Education

Department of Mathematics

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2020-02-07

## How to Cite

Hussein, B. (2020). New Conditions of The Existence of Fixed Point in Δ- Ordered Δ Banach Algebra. JOURNAL OF ADVANCES IN MATHEMATICS, 18, 60–71. https://doi.org/10.24297/jam.v18i.8370

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