*Article* **Approximation of the Fixed Point for Unified Three-Step Iterative Algorithm with Convergence Analysis in Busemann Spaces**

**Hassan Almusawa 1, Hasanen A. Hammad 2,\* and Nisha Sharma <sup>3</sup>**

	- **\*** Correspondence: hassanein\_hamad@science.sohag.edu.eg

**Abstract:** In this manuscript, a new three-step iterative scheme to approximate fixed points in the setting of Busemann spaces is introduced. The proposed algorithms unify and extend most of the existing iterative schemes. Thereafter, by making consequent use of this method, strong and Δconvergence results of mappings that satisfy the condition (E*μ*) in the framework of uniformly convex Busemann space are obtained. Our results generalize several existing results in the same direction.

**Keywords:** the condition (E*μ*); standard three-step iteration algorithm; fixed point; uniformly convex Busemann space

**MSC: AMS Subject Classification**: 47H09; 47H10; 54H25; 54E40
