A Study of Some Fixed Point Theorems Based on Various Metric Spaces

Abstract

Fixed point theory cons tutes a central theme in nonlinear analysis, serving as a newlinefounda onal tool for examining convergence, stability, and existence phenomena. newlineWhile classical results such as the Banach contrac on principle provide elegant newlinesolu ons in conven onal metric spaces, many modern problems involve uncertainty, newlinemul dimensionality, or complex-valued structures that demand broader analy cal newlineframeworks. newlineThis thesis inves gates fixed point theorems in three such generalized se ngs: G newlineMetric Spaces, Complex-Valued Metric Spaces (CVMS), and Neutrosophic Fuzzy newlineMetric Spaces (NFMS). Each framework enriches the classical metric structure G newlinemetrics by employing triplet-based distances, CVMS through complex-valued newlineformula ons, and NFMS by incorpora ng measures of truth, indeterminacy, and newlinefalsity. Within these se ngs, new contrac on principles, compa bility condi ons, newlineand operator-based generaliza ons are established, extending and unifying several newlinewell-known results. newlineThe contribu ons demonstrate that G-metrics offer effec ve tools for mul newlinedimensional convergence, CVMS provide a natural basis for modeling complex signals newlineand processes, and NFMS enable the treatment of higher-order uncertainty. newlineApplica ons are indicated in diverse fields, including engineering, control theory, newlinequantum systems, ar ficial intelligence, and bioinforma cs, where tradi onal metric newlineapproaches o en fall short. newlineBy developing generalized theorems, illustra ve examples, and construc ve newlinecorollaries, the study not only advances the theore cal scope of fixed point analysis newlinebut also emphasizes its interdisciplinary relevance. The results highlight the versa lity newlineof fixed point methods in addressing problems characterized by imprecision and newlinenonlinearity. newlineIn conclusion, this research work advances fixed point theory by systema cally newlineextending it to generalized metric structures. The findings unify rigorous mathematics with practical applications, ng the continuing relevance of fixed point newlineprinciples in addressing mod