10.30495/maca.2025.2052193.1127

Geometry of norm attainability in Orlicz spaces

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  • Mogoi N. Evans1,
  • Robert Obogi*2,
  1. Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Kenya
  2. Department of Mathematics and Actuarial Science, Kisii University, Kenya

Published in Issue 2025-01-01

How to Cite

Geometry of norm attainability in Orlicz spaces. (2025). Mathematical Analysis and Its Contemporary Applications, 7(1). https://doi.org/10.30495/maca.2025.2052193.1127

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Abstract

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.

Keywords

  • Orlicz Spaces,
  • Norm Attainability,
  • Modular Properties,
  • Convexity,
  • Nonlinear Optimization,
  • Duality Theory
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References

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