A characterization of convex φ-functions

• Autorzy: Micherda B.
• Języki publikacji: EN

Abstrakty

EN

The properties of four elements (LPFE) and (UPFE), introduced by Isac and Persson, have been recently examined in Hilbert spaces, Lp-spaces and modular spaces. In this paper we prove a new theorem showing that a modular of form ρφ(∫)= ∫ Ω φ (t,/∫(t)/)dμ(t) satisfies both (LPFE) and (UPFE) if and only if φ is convex with respect to its second variable. A connection of this result with the study of projections and antiprojections onto latticially closed subsets of the modular space Lφ is also discussed.

Słowa kluczowe

EN

inequalities; modulars; Orlicz-Musielak spaces; convexity; isotonicity; projections; antiprojections

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 1
• Strony: 171--178
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Micherda B.

• University of Bielsko-Biała Department of Mathematics and Computer Science ul. Willowa 2, 43-309 Bielsko-Biała, Poland,

Bibliografia

• [1] G. Isac, On the order monotonicity of the metric projection operator, Approximation Theory, Wavelets and Applications (Ed. S.P. Singh), Kluwer Academic Publishers, NATO ASI Series (1995), 365–379.
• [2] G. Isac, G. Lewicki, On the property of four elements in modular spaces, Acta Math. Hungar. 83 (1999) 4, 293–301.
• [3] G. Isac, L.E. Persson, On an inequality related to the isotonicity of the projection operator, J. Approx. Theory 86 (1996) 2, 129–143.
• [4] G. Isac, L.E. Persson, Inequalities related to isotonicity of projection and antiprojection operators, Math. Inequal. Appl. 1 (1998) 1, 85–97.
• [5] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, PWN, 1985.
• [6] B. Micherda, The properties of four elements in Orlicz-Musielak spaces, Math. Inequal. Appl. 4 (2001) 4, 599–608.
• [7] B. Micherda, On the latticity of projection and antiprojection sets in Orlicz-Musielak spaces, Acta Math. Hungar. 119 (2008) 1–2, 165–180.
• [8] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer-Verlag, 1983.