TY  - JOUR
ID  - Micherda2015
LB  - Micherda2015
AU  - Micherda, Bartosz
TI  - A new characterization of convex φ-functions with a parameter
ST  - A new characterization of convex φ-functions with a parameter
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 2
SP  - 191
EP  - 197
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.2.191
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.2.191
AB  - We show that, under some additional assumptions, all projection operators onto latticially closed subsets of the Orlicz-Musielak space generated by \(\Phi\) are isotonic if and only if \(\Phi\) is convex with respect to its second variable. A dual result of this type is also proven for antiprojections. This gives the positive answer to the problem presented in Opuscula Mathematica in 2012.
KW  - Orlicz-Musielak space
KW  - convex function
KW  - isotonic operator
KW  - projection operator
KW  - antiprojection operator
SN  - 1232-9274
ER  -