On the Stability and Acceleration of Projection Algorithms

Zena H. Maibed; Noor N. Salem

doi:10.30526/36.1.2923

Authors

Zena H. Maibed Department of Mathematics , College of Education for Pure Sciences,Ibn Al –Haitham, University of Baghdad
Noor N. Salem Department of Mathematics , College of Education for Pure Sciences,Ibn Al –Haitham, University of Baghdad

DOI:

https://doi.org/10.30526/36.1.2923

Keywords:

metric projection, Jungck-Picard alorithm, Jungck-normal N algorithm, , Jungck-Thianwan algorithm, Jungck-Krasnoselskii algorithm, Fixed Point

Abstract

The focus of this paper is the presentation of a new type of mapping called projection Jungck zn- Suzuki generalized and also defining new algorithms of various types (one-step and two-step algorithms) (projection Jungck-normal N algorithm, projection Jungck-Picard algorithm, projection Jungck-Krasnoselskii algorithm, and projection Jungck-Thianwan algorithm). The convergence of these algorithms has been studied, and it was discovered that they all converge to a fixed point. Furthermore, using the previous three conditions for the lemma, we demonstrated that the difference between any two sequences is zero. These algorithms' stability was demonstrated using projection Jungck Suzuki generalized mapping. In contrast, the rate of convergence of these algorithms was demonstrated by contrasting the rates of convergence of the various algorithms, leading us to conclude that the projection Jungck-normal algorithm is the fastest of all the algorithms mentioned above.

Author Biographies

Zena H. Maibed, Department of Mathematics , College of Education for Pure Sciences,Ibn Al –Haitham, University of Baghdad
Noor N. Salem, Department of Mathematics , College of Education for Pure Sciences,Ibn Al –Haitham, University of Baghdad

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