Opuscula Math. 35, no. 2 (2015), 191-197

Opuscula Mathematica

A new characterization of convex φ-functions with a parameter

Bartosz Micherda

Abstract. 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.

Keywords: Orlicz-Musielak space, convex function, isotonic operator, projection operator, antiprojection operator.

Mathematics Subject Classification: 41A65, 39B62, 46E30.

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  • Bartosz Micherda
  • University of Bielsko-Biała, Department of Mathematics, ul. Willowa 2, 43-309 Bielsko-Biała, Poland
  • Communicated by Henryk Hudzik.
  • Received: 2014-04-13.
  • Accepted: 2014-06-18.
  • Published online: 2014-11-18.
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Cite this article as:
Bartosz Micherda, A new characterization of convex φ-functions with a parameter, Opuscula Math. 35, no. 2 (2015), 191-197, http://dx.doi.org/10.7494/OpMath.2015.35.2.191

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