Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We show that, under some additional assumptions, all projection operators onto latticially closed subsets of the Orlicz-Musielak space generated by Φ are isotonic if and only if Φ 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.
Czasopismo
Rocznik
Tom
Strony
191--197
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
Bibliografia
- [1] G. Isac, On the order monotonicity of the metric projection operator, [in:] Approximation Theory, Wavelets and Applications, NATO ASI Series, Kluwer Acad. Publ., Dordrecht (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, A.B. Nemeth, Every generating isotone projection cone is latticial and correct, J. Math. Anal. Appl. 147 (1990) 1, 53-62.
- [4] G. Isac, A.B. Nemeth, Isotone projection cones in Euclidean spaces, Ann. Sci. Math. Quebec 16 (1992) 1, 35-52.
- [5] G. Isac, L.E. Persson, On an inequality related to the isotonicity of the projection operator, J. Approx. Theory 86 (1996) 2, 129-143.
- [6] G. Isac, L.E. Persson, Inequalities related to isotonicity of projection and antiprojection operators, Math. Inequal. Appl. 1 (1998) 1, 85-97.
- [7] B. Micherda, The properties of four elements in Orlicz-Musielak spaces, Math. Inequal. Appl. 4 (2001) 4, 599-608.
- [8] B. Micherda, On the latticity of projection and antiprojection sets in Orlicz-Musielak spaces, Acta Math. Hungar. 119 (2008) 1-2, 165-180.
- [9] B. Micherda, A characterization of convex ip-functions, Opuscula Math. 32 (2012) 1, 171-178.
- [10] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer-Verlag, Berlin, 1983.
- [11] M.M. Rao, Z.D. Ren, Theory of Orlicz Spaces, Monographs and Textbooks in Pure and Applied Mathematics 146, Marcel Dekker, Inc., New York, 1991.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-39a59fd8-f71a-41d9-aa2d-53c9c184c132