<![CDATA[The concept of convexity is a fundamental pillar in optimization theory and inequality analysis. This article aims to review the history and classical definition of convex functions through a literature-based approach. The literature reviewed includes works by Jensen [1], Rockafellar [2], Boyd & Vandenberghe [3], and Niculescu & Persson [4]. The analysis highlights the connection between the geometric definition of convex functions and Jensen's inequality, which demonstrates the consistency of inequality structures in both deterministic and probabilistic contexts. This study emphasizes that Jensen's inequality not only extends the concept of convex functions in probability theory but also strengthens the understanding of its geometric definition in classical analysis. This article is intended to serve as an introduction for students and researchers wishing to comprehend the foundational structure of convexity in modern mathematical theory.]]>
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