Neutrosophic Functional Analysis. Foundations, Fermatean n-Norms, and Approximation Theory

Neutrosophic Functional Analysis: Foundations, Fermatean n-Norms, and Approximation Theory presents a unified mathematical framework for the study of functional analysis under uncertainty, indeterminacy, and inconsistency by integrating neutrosophic theory with modern normed-space analysis. The book develops the fundamental concepts of neutrosophic intuitionistic algebra fuzzy normed spaces and Fermatean neutrosophic n-normed linear spaces, establishing their algebraic, topological, and geometric foundations. It systematically investigates convergence, Cauchy sequences, completeness, boundedness, compactness, neighbourhood structures, norm equivalence, and finite-dimensional properties, culminating in Heine–Borel type characterizations and compactness criteria. The theory is further extended through Banach-type fixed point theorems, contraction mappings, and applications to linear and nonlinear operator equations. A comprehensive treatment of weighted neutrosophic best approximation is also developed, including existence, Pareto efficiency, and uniqueness results under appropriate convexity assumptions. By combining classical functional analysis with neutrosophic logic and Fermatean uncertainty models, this volume provides a rigorous foundation for future research in operator theory, optimization, nonlinear analysis, approximation theory, and intelligent mathematical systems operating in uncertain environments.