Fixed Point Theory in Semigroups and Applications in Optimization Problems

Abubakar Abdulkarim; Usman Yusuf; Aminu Abdullahi; Abubakar Alhassan Muhammad; Nuraddeen Mukhtar

doi:10.62050/ljsir2025.v3n2.559

Authors

A. Abdulkarim Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria Author
Usman Yusuf Department of Mathematics, Federal University of Lafia, Nigeria Author
A. Abdullahi Department of mathematical sciences, Kaduna State University, Kaduna, Nigeria Author
A. A. Muhammad Department of Mathematics and Statistics, Nuhu Bamalli Polytechnic, Zaria, Nigeria Author
Nuraddeen Mukhtar Department of Mathematics and Statistics, Nuhu Bamalli Polytechnic, Zaria, Nigeria Author

DOI:

https://doi.org/10.62050/ljsir2025.v3n2.559

Keywords:

Fixed points, Hybrid fixed points, Semigroups, Stability, Transformation

Abstract

In this work, we introduce a new class of hybrid fixed points which arise from transformations within semigroups that exhibit both contractive and hybrid contraction properties. These fixed points have proven particularly useful in the context of optimization problems, providing a framework that guarantees convergence. The study highlights the application of hybrid fixed points in a variety of optimization schemes. By leveraging the hybrid contraction condition, it is shown that these methods offer improved stability, faster convergence, and more reliable solutions. These results are particularly significant for fields such as machine learning, where optimization algorithms often struggle with convergence issues in high dimensional spaces.

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