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A solution of an open problem concerning Lagrangian mean-type mappings

100%

Głazowska D.

Open Mathematics

2011

tom 9

nr 5

1067-1073

The problem of invariance of the geometric mean in the class of Lagrangian means was considered in [Głazowska D., Matkowski J., An invariance of geometric mean with respect to Lagrangian means, J. Math. Anal. Appl., 2007, 331(2), 1187–1199], where some necessary conditions for the generators of Lagrangian means have been established. The question if all necessary conditions are also sufficient remained open. In this paper we solve this problem.

Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu

51%

Armao F., Głazowska D., Rivas S., Rojas J.

Open Mathematics

2013

tom 11

nr 2

357-367

We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.

Ograniczanie wyników

2 Open Mathematics

2 Głazowska D.

1 Armao F.

1 Rivas S.

1 Rojas J.

1 2013

1 2011

Wyniki wyszukiwania

A solution of an open problem concerning Lagrangian mean-type mappings

Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu