OICC Press Mathematical Analysis and its Contemporary Applications 7 1 2025 01 01 Geometry of norm attainability in Orlicz spaces 10.30495/maca.2025.2052193.1127 EN Mogoi N. Evans Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Kenya Robert Obogi Department of Mathematics and Actuarial Science, Kisii University, Kenya Journal Article 2025 01 01 This paper investigates norm attainability and modular properties in Orlicz spaces, which generalize Lp-spaces and are key in functional analysis and nonlinear problems. It presents theorems on norm attainment, orthogonality, weak compactness, and uniform convexity, and introduces a novel criterion connecting the convexity of the Orlicz function with the smoothness and reflexivity of the space. The research extends classical concepts such as the ∆2-condition to ensure completeness and separability. The results have practical applications in nonlinear optimization, variational analysis, machine learning, signal processing, image reconstruction, and solving PDEs with nonlinear boundary conditions, providing a strong foundation for future research in these areas.