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Journal articles on the topic 'Functions of bounded variation'

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Published: 4 June 2021
Last updated: 30 July 2024

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1

., Jyoti. "Functions of Bounded Variation." Journal of Advances and Scholarly Researches in Allied Education 15, no. 4 (June 1, 2018): 250–52. http://dx.doi.org/10.29070/15/57855.

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2

Castillo, Mariela, Sergio Rivas, María Sanoja, and Iván Zea. "Functions of Boundedκφ-Variation in the Sense of Riesz-Korenblum." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/718507.

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We present the space of functions of boundedκφ-variation in the sense of Riesz-Korenblum, denoted byκBVφ[a,b], which is a combination of the notions of boundedφ-variation in the sense of Riesz and boundedκ-variation in the sense of Korenblum. Moreover, we prove that the space generated by this class of functions is a Banach space with a given norm and we prove that the uniformly bounded composition operator satisfies Matkowski's weak condition.
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3

Lipcsey, Z., I. M. Esuabana, J. A. Ugboh, and I. O. Isaac. "Integral Representation of Functions of Bounded Variation." Journal of Mathematics 2019 (July 8, 2019): 1–11. http://dx.doi.org/10.1155/2019/1065946.

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Functions of bounded variations form important transition between absolute continuous and singular functions. With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations. However, the determination of existence of solutions is still problematic because the solutions of differential equations is usually at least absolute continuous which is disrupted by the solutions of bounded variations. As it is known, if f:[a,bλ]→Rn is of bounded variation then f is the sum of an absolute continuous function fa and a singular function fs where the total variation of fs generates a singular measure τ and fs is absolute continuous with respect to τ. In this paper we prove that a function of bounded variation f has two representations: one is f which was described with an absolute continuous part with respect to the Lebesgue measure λ, while in the other an integral with respect to τ forms the absolute continuous part and t(τ) defines the singular measure. Both representations are obtained as parameter transformation images of an absolute continuous function on total variation domain [a,bν].
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4

Jerrard, R. L., and H. M. Soner. "Functions of bounded higher variation." Indiana University Mathematics Journal 51, no. 3 (2002): 0. http://dx.doi.org/10.1512/iumj.2002.51.2229.

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5

AISTLEITNER, CHRISTOPH, FLORIAN PAUSINGER, ANNE MARIE SVANE, and ROBERT F. TICHY. "On functions of bounded variation." Mathematical Proceedings of the Cambridge Philosophical Society 162, no. 3 (July 26, 2016): 405–18. http://dx.doi.org/10.1017/s0305004116000633.

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AbstractThe recently introduced concept of ${\mathcal D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from [20] whether every function of bounded Hardy–Krause variation is Borel measurable and has bounded ${\mathcal D}$-variation. Moreover, we show that the space of functions of bounded ${\mathcal D}$-variation can be turned into a commutative Banach algebra.
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6

Aye, Khaing Khaing, and Peng Yee Lee. "The dual of the space of functions of bounded variation." Mathematica Bohemica 131, no. 1 (2006): 1–9. http://dx.doi.org/10.21136/mb.2006.134078.

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7

Conti, Sergio, Matteo Focardi, and Flaviana Iurlano. "Which special functions of bounded deformation have bounded variation?" Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 1 (October 17, 2017): 33–50. http://dx.doi.org/10.1017/s030821051700004x.

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Functions of bounded deformation (BD) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation (BV), but are less well understood. We discuss here the relation to BV under additional regularity assumptions, which may require the regular part of the strain to have higher integrability or the jump set to have finite area or the Cantor part to vanish. On the positive side, we prove that BD functions that are piecewise affine on a Caccioppoli partition are in GSBV, and we prove that SBDp functions are approximately continuous -almost everywhere away from the jump set. On the negative side, we construct a function that is BD but not in BV and has distributional strain consisting only of a jump part, and one that has a distributional strain consisting of only a Cantor part.
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8

Ciemnoczolowski, J., and W. Orlicz. "Composing Functions of Bounded ϕ-Variation." Proceedings of the American Mathematical Society 96, no. 3 (March 1986): 431. http://dx.doi.org/10.2307/2046589.

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9

Cianchi, Andrea, and Nicola Fusco. "Functions of Bounded Variation�and Rearrangements." Archive for Rational Mechanics and Analysis 165, no. 1 (October 1, 2002): 1–40. http://dx.doi.org/10.1007/s00205-002-0214-9.

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10

Kolyada, V. I., and M. Lind. "On functions of bounded p-variation." Journal of Mathematical Analysis and Applications 356, no. 2 (August 2009): 582–604. http://dx.doi.org/10.1016/j.jmaa.2009.03.042.

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11

Colombeau, Jean François, and Arnaud Heibig. "Nonconservative Products in Bounded Variation Functions." SIAM Journal on Mathematical Analysis 23, no. 4 (July 1992): 941–49. http://dx.doi.org/10.1137/0523050.

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12

Ciemnoczołowski, J., and W. Orlicz. "Composing functions of bounded $\varphi$-variation." Proceedings of the American Mathematical Society 96, no. 3 (March 1, 1986): 431. http://dx.doi.org/10.1090/s0002-9939-1986-0822434-6.

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13

Alberico, Angela, Adele Ferone, and Roberta Volpicelli. "Functions of bounded variation and polarization." Mathematische Nachrichten 282, no. 7 (June 23, 2009): 953–63. http://dx.doi.org/10.1002/mana.200710782.

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14

Dutta, Prerona, and Khai T. Nguyen. "Covering numbers for bounded variation functions." Journal of Mathematical Analysis and Applications 468, no. 2 (December 2018): 1131–43. http://dx.doi.org/10.1016/j.jmaa.2018.08.062.

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15

LIANG, Y. S. "DEFINITION AND CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION." Fractals 25, no. 05 (September 4, 2017): 1750048. http://dx.doi.org/10.1142/s0218348x17500487.

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The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions and nondifferentiable functions. All differentiable functions are of bounded variation. Nondifferentiable functions are composed of bounded variation functions and unbounded variation functions. Fractal dimension of all bounded variation continuous functions is 1. One-dimensional unbounded variation continuous functions may have finite unbounded variation points or infinite unbounded variation points. Number of unbounded variation points of one-dimensional unbounded variation continuous functions maybe infinite and countable or uncountable. Certain examples of different one-dimensional continuous functions have been given in this paper. Thus, one-dimensional continuous functions are composed of differentiable functions, nondifferentiable continuous functions of bounded variation, continuous functions with finite unbounded variation points, continuous functions with infinite but countable unbounded variation points and continuous functions with uncountable unbounded variation points. In the end of the paper, we give an example of one-dimensional continuous function which is of unbounded variation everywhere.
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16

WU, XIAO ER, and JUN HUAI DU. "BOX DIMENSION OF HADAMARD FRACTIONAL INTEGRAL OF CONTINUOUS FUNCTIONS OF BOUNDED AND UNBOUNDED VARIATION." Fractals 25, no. 03 (May 18, 2017): 1750035. http://dx.doi.org/10.1142/s0218348x17500359.

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The present paper investigates fractal dimension of Hadamard fractional integral of continuous functions of bounded and unbounded variation. It has been proved that Hadamard fractional integral of continuous functions of bounded variation still is continuous functions of bounded variation. Definition of an unbounded variation point has been given. We have proved that Box dimension and Hausdorff dimension of Hadamard fractional integral of continuous functions of bounded variation are [Formula: see text]. In the end, Box dimension and Hausdorff dimension of Hadamard fractional integral of certain continuous functions of unbounded variation have also been proved to be [Formula: see text].
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17

Kanas, Stanisława, and Şahsene Altinkaya. "Functions of bounded variation related to domains bounded by conic sections." Mathematica Slovaca 69, no. 4 (August 27, 2019): 833–42. http://dx.doi.org/10.1515/ms-2017-0272.

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Abstract The aim of this paper is to bring together two areas of studies in the theory of analytic functions: functions of bounded variation and functions related to domains bounded by conic sections. Some relevant properties are indicated.
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18

Leiva, Hugo, Nelson Merentes, Sergio T. Rivas, José Sánchez, and Małgorzata Wróbel. "On Functions of Bounded (φ, k)-Variation." Tatra Mountains Mathematical Publications 74, no. 1 (December 1, 2019): 91–116. http://dx.doi.org/10.2478/tmmp-2019-0023.

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Abstract Given a φ-function φ and k ∈ ℕ, we introduce and study the concept of (φ, k)-variation in the sense of Riesz of a real function on a compact interval. We show that a function u :[a, b] → ℝ has a bounded (φ, k)-variation if and only if u(k−1) is absolutely continuous on [a, b]and u(k) belongs to the Orlicz class L φ[a, b]. We also show that the space generated by this class of functions is a Banach space. Our approach simultaneously generalizes the concepts of the Riesz φ-variation, the de la Vallée Poussin second-variation and the Popoviciu kth variation.
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19

Mukhopadhyay, S., and D. Sain. "On functions of bounded n-th variation." Fundamenta Mathematicae 131, no. 3 (1988): 191–208. http://dx.doi.org/10.4064/fm-131-3-191-208.

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20

Pierce and Waterman. "FUNCTIONS OF BOUNDED VARIATION IN THE MEAN." Real Analysis Exchange 24, no. 1 (1998): 41. http://dx.doi.org/10.2307/44152914.

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21

Hallenbeck, D. J., and K. Samotij. "On radial variation of bounded analytic functions." Complex Variables, Theory and Application: An International Journal 15, no. 1 (June 1990): 43–52. http://dx.doi.org/10.1080/17476939008814432.

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22

Merentes, N., S. Rivas, and J. L. Sanchez. "On Functions of Bounded(p,k)-Variation." Journal of Function Spaces and Applications 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/202987.

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We introduce and study the concept of(p,k)-variation (1<p<∞,k∈N)of a real function on a compact interval. In particular, we prove that a functionu:[a,b]→Rhas bounded(p,k)-variation if and only ifu(k-1)is absolutely continuous on[a,b]andu(k)belongs toLp[a,b]. Moreover, an explicit connection between the(p,k)-variation ofuand theLp-norm ofu(k)is given which is parallel to the classical Riesz formula characterizing functions in the spacesRVp[a,b]andAp[a,b]. This may also be considered as an alternative characterization of the one variable Sobolev spaceWpk[a,b].
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23

Traub, J. F., and D. Lee. "Optimal integration for functions of bounded variation." Mathematics of Computation 45, no. 172 (1985): 505. http://dx.doi.org/10.1090/s0025-5718-1985-0804939-4.

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24

Noll, Walter, and Epifanio G. Virga. "Fit regions and functions of bounded variation." Archive for Rational Mechanics and Analysis 102, no. 1 (March 1988): 1–21. http://dx.doi.org/10.1007/bf00250921.

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25

Prestin, J. "Lagrange interpolation for functions of bounded variation." Acta Mathematica Hungarica 62, no. 1-2 (March 1993): 1–13. http://dx.doi.org/10.1007/bf01874212.

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26

Elcrat, Alan, and Ray Treinen. "Floating Drops and Functions of Bounded Variation." Complex Analysis and Operator Theory 5, no. 1 (July 25, 2009): 299–311. http://dx.doi.org/10.1007/s11785-009-0032-2.

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27

Megrelishvili, Michael. "Median pretrees and functions of bounded variation." Topology and its Applications 285 (November 2020): 107383. http://dx.doi.org/10.1016/j.topol.2020.107383.

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28

Barza, Sorina, and Pilar Silvestre. "Functions of bounded second $$p$$ p -variation." Revista Matemática Complutense 27, no. 1 (September 28, 2013): 69–91. http://dx.doi.org/10.1007/s13163-013-0136-0.

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29

Fukuyama, Katusi. "Gap series and functions of bounded variation." Acta Mathematica Hungarica 110, no. 3 (February 2006): 175–91. http://dx.doi.org/10.1007/s10474-006-0014-z.

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30

Pan, Cheng-Han. "Nowhere-monotone differentiable functions and bounded variation." Journal of Mathematical Analysis and Applications 494, no. 2 (February 2021): 124618. http://dx.doi.org/10.1016/j.jmaa.2020.124618.

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31

Richman, Fred. "Omniscience Principles and Functions of Bounded Variation." MLQ 48, no. 1 (January 2002): 111–16. http://dx.doi.org/10.1002/1521-3870(200201)48:1<111::aid-malq111>3.0.co;2-6.

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32

Mukhopadhyay, S. K., and S. N. Mukhopadhyay. "Functions of bounded kth variation and absolutely kth continuous functions." Bulletin of the Australian Mathematical Society 46, no. 1 (August 1992): 91–106. http://dx.doi.org/10.1017/s0004972700011709.

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33

Meng, Xiangling, Yu Liu, and Xiangyun Xie. "Capacity and the Corresponding Heat Semigroup Characterization from Dunkl-Bounded Variation." Fractal and Fractional 5, no. 4 (December 18, 2021): 280. http://dx.doi.org/10.3390/fractalfract5040280.

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In this paper, we study some important basic properties of Dunkl-bounded variation functions. In particular, we derive a way of approximating Dunkl-bounded variation functions by smooth functions and establish a version of the Gauss–Green Theorem. We also establish the Dunkl BV capacity and investigate some measure theoretic properties, moreover, we show that the Dunkl BV capacity and the Hausdorff measure of codimension one have the same null sets. Finally, we develop the characterization of a heat semigroup of the Dunkl-bounded variation space, thereby giving its relation to the functions of Dunkl-bounded variation.
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34

Noor, Khalida, Nazar Khan, and Muhammad Noor. "On generalized spiral-like analytic functions." Filomat 28, no. 7 (2014): 1493–503. http://dx.doi.org/10.2298/fil1407493n.

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In this paper, we use the concept of bounded Mocanu variation to introduce a new class of analytic functions, defined in the open unit disc, which unifies a number of classes previously studied such as those of functions with bounded radius rotation and bounded Mocanu variation. It also generalizes the concept of ?-spiral likeness in some sense. Some interesting properties of this class including inclusion results, arclength problems and a sufficient condition for univalency are studied.
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35

Berman, Robert D. "Generalized Variation and Functions of Slow Growth." Canadian Journal of Mathematics 40, no. 1 (February 1, 1988): 55–85. http://dx.doi.org/10.4153/cjm-1988-003-7.

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Many of the basic results of HP theory on the disk Δ = {|z| < 1} are proved using the Cauchy-Stieltjes representation1.1and the Poisson-Stieltjes representation1.2Here, μ:R → C is a complex-valued function of a real variable that is of bounded variation on [0, 2π] such that μ(t + 2π) = μ(t) + μ(2t) — μ(0), t ∊ R,is the Cauchy kernel, andis the Poisson kernel. It is therefore natural to generalize these representations in such a way that some of the basic properties and results carry over. Such a generalization occurs when the assumption that μ is of bounded variation on [0, 2μ] is replaced by the requirement that it is measurable and bounded on [0, 2μ] (cf. [9]). The integrals in (1.1) and (1.2) are then defined by a formal integration by parts. After some preliminaries in Section 2, we catalogue a variety of results which remain valid in Section 3.
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36

Dziok, Jacek. "Characterizations of analytic functions associated with functions of bounded variation." Annales Polonici Mathematici 109, no. 2 (2013): 199–207. http://dx.doi.org/10.4064/ap109-2-7.

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37

Duchoˇn, Miloslav, and Camille Debiève. "Functions with bounded variation in locally convex space." Tatra Mountains Mathematical Publications 49, no. 1 (December 1, 2011): 89–98. http://dx.doi.org/10.2478/v10127-011-0028-y.

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ABSTRACT The present paper is concerned with some properties of functions with values in locally convex vector space, namely functions having bounded variation and generalizations of some theorems for functions with values in locally convex vector spaces replacing Banach spaces, namely Theorem: If X is a sequentially complete locally convex vector space, then the function x(・) : [a, b] → X having a bounded variation on the interval [a, b] defines a vector-valued measure m on borelian subsets of [a, b] with values in X and with the bounded variation on the borelian subsets of [a, b]; the range of this measure is also a weakly relatively compact set in X. This theorem is an extension of the results from Banach spaces to locally convex spaces.
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38

Prajapati, Jyotindra C., and Krunal B. Kachhia. "Functions of bounded fractional differential variation – A new concept." Georgian Mathematical Journal 23, no. 3 (September 1, 2016): 417–27. http://dx.doi.org/10.1515/gmj-2016-0030.

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AbstractThe idea of functions of bounded differential variation was introduced by Bhatt, Dabhi and Kachhia in [2]. In the present paper, we introduce functions of bounded fractional differential variation using the Caputo-type fractional derivative instead of the commonly used first-order derivative. Various properties and relation with some known results of classical analysis are also studied. We prove that the space ${\mathrm{BFDV}[a,b]}$ of all functions of bounded fractional differential variation on ${[a,b]}$ is a normed algebra under certain type of norms.
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39

LIU, XING, JUN WANG, and HE LIN LI. "THE CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS AND THEIR FRACTIONAL INTEGRAL." Fractals 26, no. 05 (October 2018): 1850063. http://dx.doi.org/10.1142/s0218348x18500639.

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This paper mainly discusses the continuous functions whose fractal dimension is 1 on [Formula: see text]. First, we classify continuous functions into unbounded variation and bounded variation. Then we prove that the fractal dimension of both continuous functions of bounded variation and their fractional integral is 1. As for continuous functions of unbounded variation, we solve several special types. Finally, we give the example of one-dimensional continuous function of unbounded variation.
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40

Budak, Hüseyin, and Abd-Allah Hyder. "Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities." AIMS Mathematics 8, no. 12 (2023): 30760–76. http://dx.doi.org/10.3934/math.20231572.

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<abstract><p>In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions, Lipschitzian functions and functions of bounded variation. To accomplish our objective, we begin by establishing a crucial identity for differentiable functions. Leveraging this identity, we subsequently derive new variations of fractional Milne inequalities.</p></abstract>
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41

Bracamonte, Mireya, José Giménez, and Nelson Merente. "Vector valued functions of bounded bidimensional $\Phi$-variation." Annals of Functional Analysis 4, no. 1 (2013): 89–108. http://dx.doi.org/10.15352/afa/1399899839.

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42

Gora, Pawel, and Abraham Boyarsky. "On Functions of Bounded Variation in Higher Dimensions." American Mathematical Monthly 99, no. 2 (February 1992): 159. http://dx.doi.org/10.2307/2324185.

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43

Prestin, Jürgen, and Manfred Tasche. "Trigonometric interpolation for bivariate functions of bounded variation." Banach Center Publications 22, no. 1 (1989): 309–21. http://dx.doi.org/10.4064/-22-1-309-321.

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44

Gogoladze, L. D., and V. Sh Tsagareishvili. "The Fourier coefficients of functions with bounded variation." Russian Mathematics 57, no. 8 (July 31, 2013): 10–19. http://dx.doi.org/10.3103/s1066369x13080021.

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45

Prus-Wisniowski, Franciszek. "On Superposition of Functions of Bounded ϕ-Variation." Proceedings of the American Mathematical Society 107, no. 2 (October 1989): 361. http://dx.doi.org/10.2307/2047825.

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46

Breit, Dominic, Lars Diening, and Franz Gmeineder. "The Lipschitz truncation of functions of bounded variation." Indiana University Mathematics Journal 70, no. 6 (2021): 2237–60. http://dx.doi.org/10.1512/iumj.2021.70.8742.

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47

Russell. "BANACH ALGEBRAS OF FUNCTIONS HAVING GENERALIZED BOUNDED VARIATION." Real Analysis Exchange 12, no. 1 (1986): 126. http://dx.doi.org/10.2307/44151783.

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48

Cater. "ON THE DERIVATIVES OF FUNCTIONS OF BOUNDED VARIATION." Real Analysis Exchange 26, no. 2 (2000): 923. http://dx.doi.org/10.2307/44154092.

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49

Cater. "ON THE DERIVATIVES OF FUNCTIONS OF BOUNDED VARIATION." Real Analysis Exchange 26, no. 2 (2000): 975. http://dx.doi.org/10.2307/44154097.

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50

Ambrosio, Luigi, and Francesco Ghiraldin. "Compactness of Special Functions of Bounded Higher Variation." Analysis and Geometry in Metric Spaces 1 (January 4, 2013): 1–30. http://dx.doi.org/10.2478/agms-2012-0001.

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Abstract Given an open set Ω ⊂ Rm and n > 1, we introduce the new spaces GBnV(Ω) of Generalized functions of bounded higher variation and GSBnV(Ω) of Generalized special functions of bounded higher variation that generalize, respectively, the space BnV introduced by Jerrard and Soner in [43] and the corresponding SBnV space studied by De Lellis in [24]. In this class of spaces, which allow as in [43] the description of singularities of codimension n, the distributional jacobian Ju need not have finite mass: roughly speaking, finiteness of mass is not required for the (m−n)-dimensional part of Ju, but only finiteness of size. In the space GSBnV we are able to provide compactness of sublevel sets and lower semicontinuity of Mumford-Shah type functionals, in the same spirit of the codimension 1 theory [5,6].
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