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

100%

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.

The Basic Existence Theorem of Riemann-Stieltjes Integral

100%

Nakasho K., Narita K., Shidama Y.

Formalized Mathematics

2016

tom 24

nr 4

253-259

In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are based on [15], [12], [10], and [11].

Ograniczanie wyników

1 Formalized Mathematics

1 Open Mathematics

1 Armao F.

1 Głazowska D.

1 Nakasho K.

1 Narita K.

1 Rivas S.

1 Rojas J.

1 Shidama Y.

1 2016

1 2013

Wyniki wyszukiwania

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

The Basic Existence Theorem of Riemann-Stieltjes Integral