Generalized Exponential (Euler-Type) Inequalities: Theory, Proofs, and Applications

This paper introduces a universal framework for generalized exponential (Euler-type) inequalities, extending classical results such as Jensen’s and the Arithmetic-Geometric Mean (AM-GM) inequalities. We provide a comprehensive mathematical formulation, rigorous proofs, special cases, and discuss applications in sequence symmetry, topological dynamics, artificial intelligence, and mathematical physics. The results allow for new insights in both abstract and applied mathematics.The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this workl