10.30495/maca.2025.2056607.1133

Norm attainment and structural properties in Orlicz spaces: A comprehensive study on strict convexity, duality, and optimization

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  • Mogoi N. Evans1,
  • Robert Obogi2,
  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 2025-08-28

How to Cite

Norm attainment and structural properties in Orlicz spaces: A comprehensive study on strict convexity, duality, and optimization. (2025). Mathematical Analysis and Its Contemporary Applications, 7(3). https://doi.org/10.30495/maca.2025.2056607.1133

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Abstract

We investigate norm attainability and duality properties in Orlicz spaces, extending classical results from Banach and Hilbert spaces to a more gen- eral functional framework. We establish 14 fundamental theorems that character- ize norm attainment in terms of strict convexity, uniform convexity, and weak con- vergence. We explore the duality structure of Orlicz spaces, highlighting key differ- ences from Lp spaces and providing a variational characterization of the norm. We also discuss applications in optimization and variational problems, demonstrating the significance of norm-attaining functionals in these settings. Our findings con- tribute to a deeper understanding of Orlicz space geometry and its implications for functional analysis and applied mathematics.

Keywords

  • Orlicz spaces,
  • norm attainability,
  • duality properties,
  • convexity,
  • functional analysis
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References

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