The relation between Fα – absolutely continuous of order α ∈ (0, 1) and function of bounded variation

2020 ◽  
Author(s):  
Supriyadi Wibowo ◽  
V. Y. Kurniawan ◽  
Siswanto
Keyword(s):  
Bounded Variation ◽  
Function Of Bounded Variation ◽  
Absolutely Continuous ◽  
And Function

scholarly journals Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation

2005 ◽  
Vol 2005 (23) ◽  
pp. 3827-3833 ◽  
Author(s):  
Vijay Gupta ◽  
Ulrich Abel ◽  
Mircea Ivan
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Function Of Bounded Variation ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of

We study the approximation properties of beta operators of second kind. We obtain the rate of convergence of these operators for absolutely continuous functions having a derivative equivalent to a function of bounded variation.

The Factorisation of the rectangular distribution

1967 ◽  
Vol 4 (3) ◽  
pp. 529-542 ◽  
Author(s):  
T. Lewis
Keyword(s):  
Bounded Variation ◽  
Distribution Functions ◽  
Absolutely Continuous ◽  
Rectangular Distribution ◽  
Factor Type

Questions of the decomposability of distribution functions into real-valued components of bounded variation were discussed by P. Lévy (1964) in relation to the nature of the components, whether non-decreasing (distribution functions in particular) or absolutely continuous (a.c.) or both. Hanson (1965), in a review of Lévy's paper, raised the question of whether or not a rectangular distribution could be decomposed into two a.c. distributions. In fact, D. G. Kendall had conjectured earlier (Kendall (1960)) that no such decomposition is possible. The object of this paper is to state and prove the truth of Kendall's conjecture. “Decomposition” or “factorisation” will be understood throughout the paper to mean decomposition into distributions. Decompositions of the rectangular distribution into one a.c. and one discrete factor are well known (see, e.g., Lukacs (1960) pp. 128–9), and decompositions in which both factors are singular continuous (s.c.) have been discovered by Kendall and by P. M. Lee; it is shown here that no other combinations of factor-type can exist. References to other work on related decomposability properties are given in the papers by Lévy and Kendall cited above.

scholarly journals On second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 56 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

Abstract This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem $$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$ where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.

scholarly journals Equilibrium states for piecewise monotonic transformations

1982 ◽  
Vol 2 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Franz Hofbauer ◽  
Gerhard Keller
Keyword(s):  
Periodic Orbits ◽  
Bounded Variation ◽  
Critical Points ◽  
Equilibrium States ◽  
Absolutely Continuous ◽  
Specification Property ◽  
Ergodic Properties ◽  
Piecewise Monotonic

AbstractWe show that equilibrium states μ of a function φ on ([0,1], T), where T is piecewise monotonic, have strong ergodic properties in the following three cases:(i) sup φ — inf φ <htop(T) and φ is of bounded variation.(ii) φ satisfies a variation condition and T has a local specification property.(iii) φ = —log |T′|, which gives an absolutely continuous μ, T is C2, the orbits of the critical points of T are finite, and all periodic orbits of T are uniformly repelling.

scholarly journals The Nemitskij operator on Lipk-type and BVk-type spaces

2013 ◽  
Vol 46 (3) ◽  
Author(s):  
José Giménez ◽  
Lorena López ◽  
N. Merentes
Keyword(s):  
Bounded Variation ◽  
Continuous Functions ◽  
Function Spaces ◽  
Compact Interval ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Type Spaces

AbstractIn this paper, we discuss and present various results about acting and boundedness conditions of the autonomous Nemitskij operator on certain function spaces related to the space of all real valued Lipschitz (of bounded variation, absolutely continuous) functions defined on a compact interval of ℝ. We obtain a result concerning the integrability of products of the form

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