OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 15 3 2025 05 30 Convergence and Stability Analysis of Particle Swarm Optimization Using The Fixed Point Method 89 99 10.71932/ijm.2025.1081384 EN H Akewe Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria. E. P.Fasina Department of Computer Sciences, University of Lagos, Lagos, Nigeria. B. A.Sawyerr Department of Computer Sciences, University of Lagos, Lagos, Nigeria. Journal Article 2025 05 30 This paper presents a fixed point analytical approach to one of the most commonly used optimization techniques known as particle swarm optimization (PSO) and established that the solution space of PSO is a Banach space. With the help of well constructed fixed point theorem, the iterative intelligence algorithm of the PSO was shown to converge to the unique global fixed point. The PSO iterative algorithm was further proven to be $T$-stable. An example was provided and used to demonstrate the applicablity of the stability result. Our results complement other methods of obtaining solutions for PSO in the literature.