TY  - JOUR
ID  - Micherda2012
LB  - Micherda2012
AU  - Micherda, Bartosz
TI  - A characterization of convex φ-functions
ST  - A characterization of convex φ-functions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 1
SP  - 171
EP  - 178
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.1.171
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.1.171
AB  - 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.
KW  - inequalities
KW  - modulars
KW  - Orlicz-Musielak spaces
KW  - convexity
KW  - isotonicity
KW  - antiprojections
SN  - 1232-9274
ER  -