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Abstract
In this study, we explore the concept of Strong and Weak Neutrosophic Schauder bases in the context of functional analysis. Neutrosophic logic, which generalizes fuzzy and intuitionistic fuzzy logic, allows for handling indeterminacies. We extend this to Schauder bases, which are fundamental tools in the study of Banach spaces, by incorporating neutrosophic components to capture uncertainty, imprecision, and vagueness in the approximation of elements within these spaces. We define both strong and weak Neutrosophic Schauder bases and investigate their properties, convergence behavior, and relationships with classical Schauder bases. Our results contribute to the understanding of approximation theory in spaces where uncertainty plays a critical role, offering new insights into both theoretical and applied mathematics, particularly in areas such as decision theory, optimization, and computational analysis where neutrosophic logic is increasingly relevant.
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