Convex functional analysis

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This book developed over several years as the authors taught variational calculus and applied functional analysis to graduate students in engineering and mathematics. It reflects their research in applying functional analytic principles to variational calculus, mechanics, and control theory. A significant challenge in employing functional, convex, and set-valued analysis for practical engineering and physics problems is the overwhelming number of definitions, lemmas, theorems, and propositions that form the foundation of functional analysis. Despite its complexity, functional analysis is a powerful tool for addressing practical issues in mechanics and physics. However, many academics spend their careers immersed in abstract mathematics, which demands discipline and dedication. Mathematics is often likened to a pyramid of knowledge, where understanding builds layer by layer. The challenge arises because engineers and scientists typically wish to begin their learning "above the base" of this pyramid. They are generally less focused on the intricacies of axiomatic theorem derivation and more interested in acquiring a practical understanding of how the theory applies to their specific fields.