Fixed Point Theory in Semigroups and Applications in Optimization Problems

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.