Displaying similar documents to “A full characterization of multipliers for the strong ρ -integral in the euclidean space”

The M α and C -integrals

Jae Myung Park, Hyung Won Ryu, Hoe Kyoung Lee, Deuk Ho Lee (2012)

Czechoslovak Mathematical Journal

Similarity:

In this paper, we define the M α -integral of real-valued functions defined on an interval [ a , b ] and investigate important properties of the M α -integral. In particular, we show that a function f : [ a , b ] → R is M α -integrable on [ a , b ] if and only if there exists an A C G α function F such that F ' = f almost everywhere on [ a , b ] . It can be seen easily that every McShane integrable function on [ a , b ] is M α -integrable and every M α -integrable function on [ a , b ] is Henstock integrable. In addition, we show that the M α -integral is equivalent to...

Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

Similarity:

It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f [ 0 , 1 ] 2 ⟶ ℝ and a continuous function F [ 0 , 1 ] 2 ⟶ ℝ such that ( ) ∫ 0 x ( ) ∫ 0 y f ( u , v ) d v d u = ( ) ∫ 0 y ( ) ∫ 0 x f ( u , v ) d u d v = F ( x , y ) for all ( x , y ) ∈ [ 0 , 1 ] 2 .

Convergence of ap-Henstock-Kurzweil integral on locally compact spaces

Hemanta Kalita, Ravi P. Agarwal, Bipan Hazarika (2025)

Czechoslovak Mathematical Journal

Similarity:

We introduce an ap-Henstock-Kurzweil type integral with a non-atomic Radon measure and prove the Saks-Henstock type lemma. The monotone convergence theorem, μ ap -Henstock-Kurzweil equi-integrability, and uniformly strong Lusin condition are discussed.

Cauchy's residue theorem for a class of real valued functions

Branko Sarić (2010)

Czechoslovak Mathematical Journal

Similarity:

Let [ a , b ] be an interval in ℝ and let F be a real valued function defined at the endpoints of [ a , b ] and with a certain number of discontinuities within [ a , b ] . Assuming F to be differentiable on a set [ a , b ] ∖ E to the derivative f , where E is a subset of [ a , b ] at whose points F can take values ± ∞ or not be defined at all, we adopt the convention that F and f are equal to 0 at all points of E and show that 𝒦ℋ -vt ∫ a b f = F ( b ) - F ( a ) , where 𝒦ℋ -vt denotes the total value of the integral. The paper ends with a few examples that illustrate the...

On a generalization of Henstock-Kurzweil integrals

Jan Malý, Kristýna Kuncová (2019)

Mathematica Bohemica

Similarity:

We study a scale of integrals on the real line motivated by the M C α integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.

The L r Henstock-Kurzweil integral

Paul M. Musial, Yoram Sagher (2004)

Studia Mathematica

Similarity:

We present a method of integration along the lines of the Henstock-Kurzweil integral. All L r -derivatives are integrable in this method.