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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Breckner, W. W.,Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen. Publ. Inst. Math.23 (1978), 13–20.
Matuszewska, W. andOrlicz, W.,A note on the theory of s-normed spaces of ϕ-integrable functions. Studia Math.21 (1961), 107–115.
Musielak, J.,Orlicz spaces and modular spaces. [Lecture Notes in Math. Vol. 1034]. Springer-Verlag, Berlin, 1983.
Orlicz, W.,A note on modular spaces. I. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.9 (1961), 157–162.
Rolewicz, S.,Metric linear spaces, 2nd Ed. PWN, Warszawa, 1984.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hudzik, H., Maligranda, L. Some remarks ons-convex functions. Aeq. Math. 48, 100–111 (1994). https://doi.org/10.1007/BF01837981
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01837981