A STUDY OF HYBRID FIXED POINTS ON SEMIGROUPS OF TRANSFORMATION

Abstract

Fixed point theory plays a fundamental role in mathematical analysis, algebra, and topology, with applications spanning differential equations, game theory, and computer science. This study extends classical fixed point results by exploring hybrid fixed points within semigroups of transformation. Hybrid fixed points generalize standard fixed points by incorporating auxiliary functions, allowing for broader applications in iterative methods and computational mathematics. We establish key results on hybrid fixed points by considering contractive and nonexpansive mappings in semigroups. Using Banach’s contraction principle and related fixed point theorems, we prove the existence and uniqueness of hybrid fixed points under suitable conditions. Notable results include hybrid contractions, asymptotic regularity, and their implications in complete and compact metric spaces. Examples illustrate the theoretical findings, demonstrating hybrid fixed points in transformation semigroups.