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aequationes mathematicae

, Volume 48, Issue 1, pp 100–111 | Cite as

Some remarks ons-convex functions

  • H. Hudzik
  • L. Maligranda
Research Papers

Summary

Two kinds ofs-convexity (0 <s ≤ 1) are discussed. It is proved among others thats-convexity in the second sense is essentially stronger than thes-convexity in the first, original, sense whenever 0 <s < 1. Some properties ofs-convex functions in both senses are considered and various examples and counterexamples are given.

AMS (1991) subject classification

26A51 

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References

  1. [1]
    Breckner, W. W.,Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen. Publ. Inst. Math.23 (1978), 13–20.Google Scholar
  2. [2]
    Matuszewska, W. andOrlicz, W.,A note on the theory of s-normed spaces of ϕ-integrable functions. Studia Math.21 (1961), 107–115.Google Scholar
  3. [3]
    Musielak, J.,Orlicz spaces and modular spaces. [Lecture Notes in Math. Vol. 1034]. Springer-Verlag, Berlin, 1983.Google Scholar
  4. [4]
    Orlicz, W.,A note on modular spaces. I. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.9 (1961), 157–162.Google Scholar
  5. [5]
    Rolewicz, S.,Metric linear spaces, 2nd Ed. PWN, Warszawa, 1984.Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • H. Hudzik
    • 1
    • 2
  • L. Maligranda
    • 1
    • 2
  1. 1.Institute of MathematicsA. Mickiewicz UniversityPoznanPoland
  2. 2.Department of MathematicsLuleå UniversityLuleåSweden

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