Calculation of improper integrals using uniformly distributed sequences
Cauchy problem with Denjoy-Stieltjes integral
This work is devoted to analyzing the existence of the Cauchy fractional-type problems considering the Riemann-Liouville derivative (in the distributional Denjoy integral sense) of real order . These kinds of equations are a generalization of the measure differential equations. Our results extend A. A. Kilbas, H. M. Srivastava, J. J. Trujillo (2006) and H. Zhou, G. Ye, W. Liu, O. Wang (2015).
Cesàro-Perron-Stieltjes integral
Chain rules and p-variation
The main result is a Young-Stieltjes integral representation of the composition ϕ ∘ f of two functions f and ϕ such that for some α ∈ (0,1], ϕ has a derivative satisfying a Lipschitz condition of order α, and f has bounded p-variation for some p < 1 + α. If given α ∈ (0,1], the p-variation of f is bounded for some p < 2 + α, and ϕ has a second derivative satisfying a Lipschitz condition of order α, then a similar result holds with the Young-Stieltjes integral replaced by its extension.
Compact operators and integral equations in the space
The space of Henstock-Kurzweil integrable functions on is the uncountable union of Fréchet spaces . In this paper, on each Fréchet space , an -norm is defined for a continuous linear operator. Hence, many important results in functional analysis, like the Banach-Steinhaus theorem, the open mapping theorem and the closed graph theorem, hold for the space. It is known that every control-convergent sequence in the space always belongs to a space for some . We illustrate how to apply results...
Compactifications, Hartman functions and (weak) almost periodicity [Book]
Comparison theorems of isoperimetric type for moments of compact sets.
A unified approach to prove isoperimetric inequalities for moments and basic inequalities of interpolation spaces L(p,q) is developed. Instead symmetrization methods we use a monotonicity property of special Stiltjes' means.
Concerning the existence of the double Stieltjes mean -integral
Continuous dependence of inverse fundamental matrices of generalized linear ordinary differential equations on a parameter
The problem of continuous dependence for inverses of fundamental matrices in the case when uniform convergence is violated is presented here.
Convergence presque sûre de moyennes de sommes de Riemann
Convergence theorems for a Daniell-Loomis integral.