@Article{Micherda2012,
author = "Micherda, Bartosz",
title = "A characterization of convex φ-functions",
journal = "Opuscula Math.",
year = "2012",
volume = "32",
number = "1",
pages = "171--178",
doi = "http://dx.doi.org/10.7494/OpMath.2012.32.1.171",
url = "http://dx.doi.org/10.7494/OpMath.2012.32.1.171",
abstract = "The properties of four elements \((LPFE)\) and \((UPFE)\), introduced by Isac and Persson, have been recently examined in Hilbert spaces, \(L^p\)-spaces and modular spaces. In this paper we prove a new theorem showing that a modular of form \(\rho_{\Phi}(f)=\int_{\Omega}\Phi(t,|f(t)|)d\mu(t)\) satisfies both \((LPFE)\) and \((UPFE)\) if and only if \(\Phi\) 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 \(L^{\Phi}\) is also discussed.",
keywords = "inequalities, modulars, Orlicz-Musielak spaces, convexity, isotonicity, antiprojections",
issn = "1232-9274"
}