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Journal articles on the topic 'Bounded variation'

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Published: 4 June 2021
Last updated: 1 February 2022

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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

Foran. "BOUNDED VARIATION AND POROSITY." Real Analysis Exchange 12, no. 2 (1986): 468. http://dx.doi.org/10.2307/44153590.

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4

Giménez, José, Lorena López, N. Merentes, and J. L. Sánchez. "On Bounded Second Variation." Advances in Pure Mathematics 02, no. 01 (2012): 22–26. http://dx.doi.org/10.4236/apm.2012.21005.

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5

Chistyakov, V. V. "Selections of Bounded Variation." Journal of Applied Analysis 10, no. 1 (January 2004): 1–82. http://dx.doi.org/10.1515/jaa.2004.1.

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6

Hencl, Stanislav, Pekka Koskela, and Jani Onninen. "Homeomorphisms of Bounded Variation." Archive for Rational Mechanics and Analysis 186, no. 3 (October 16, 2007): 351–60. http://dx.doi.org/10.1007/s00205-007-0056-6.

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7

Vinter, R. B. "Multifunctions of bounded variation." Journal of Differential Equations 260, no. 4 (February 2016): 3350–79. http://dx.doi.org/10.1016/j.jde.2015.10.033.

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8

Gulgowski, Jacek. "On integral bounded variation." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113, no. 2 (December 22, 2017): 399–422. http://dx.doi.org/10.1007/s13398-017-0482-8.

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9

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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10

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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11

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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12

Prus-Wisniowski, Franciszek. "On Ordered Λ-Bounded Variation." Proceedings of the American Mathematical Society 109, no. 2 (June 1990): 375. http://dx.doi.org/10.2307/2047998.

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13

Kita, H., and K. Yoneda. "A generalization of bounded variation." Acta Mathematica Hungarica 56, no. 3-4 (September 1990): 229–38. http://dx.doi.org/10.1007/bf01903837.

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14

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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15

Pierce, Pamela B., and Daniel Waterman. "Bounded variation in the mean." Proceedings of the American Mathematical Society 128, no. 9 (February 21, 2000): 2593–96. http://dx.doi.org/10.1090/s0002-9939-00-05391-0.

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16

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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17

Prus-Wi{śniowski, Franciszek. "On ordered $\Lambda$-bounded variation." Proceedings of the American Mathematical Society 109, no. 2 (February 1, 1990): 375. http://dx.doi.org/10.1090/s0002-9939-1990-1004422-3.

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18

Bourgain, J. "Bounded variation of measure convolutions." Mathematical Notes 54, no. 4 (October 1993): 995–1001. http://dx.doi.org/10.1007/bf01210418.

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19

Bugajewska, Daria, and Piotr Kasprzak. "On bounded lower Λ-variation." Journal of Mathematical Analysis and Applications 423, no. 1 (March 2015): 561–93. http://dx.doi.org/10.1016/j.jmaa.2014.09.072.

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20

Chistyakov, V. V. "On mappings of bounded variation." Journal of Dynamical and Control Systems 3, no. 2 (June 1997): 261–89. http://dx.doi.org/10.1007/bf02465896.

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21

Das. "GENERALIZED BOUNDED VARIATION AND GENERALIZED INTEGRALS." Real Analysis Exchange 21, no. 1 (1995): 65. http://dx.doi.org/10.2307/44153878.

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22

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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23

Pérez-Abreu, Victor, and Alfonso Rocha-Arteaga. "On stable processes of bounded variation." Statistics & Probability Letters 33, no. 1 (April 1997): 69–77. http://dx.doi.org/10.1016/s0167-7152(96)00111-3.

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24

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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25

Aviles, Patricio, and Yoshikazu Giga. "integrals on mappings of bounded variation." Duke Mathematical Journal 67, no. 3 (September 1992): 517–38. http://dx.doi.org/10.1215/s0012-7094-92-06720-2.

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26

Chaparro, Héctor Camilo. "On multipliers between bounded variation spaces." Annals of Functional Analysis 9, no. 3 (August 2018): 376–83. http://dx.doi.org/10.1215/20088752-2017-0047.

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27

Kindermann, Stefan. "Bounded Variation Regularization Using Line Sections." Numerical Functional Analysis and Optimization 30, no. 3-4 (April 17, 2009): 259–88. http://dx.doi.org/10.1080/01630560902841161.

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28

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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29

Gousseau, Yann, and Jean-Michel Morel. "Are Natural Images of Bounded Variation?" SIAM Journal on Mathematical Analysis 33, no. 3 (January 2001): 634–48. http://dx.doi.org/10.1137/s0036141000371150.

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30

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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31

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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32

Castillo, René Erlín, Nelson Merentes, and Humberto Rafeiro. "Bounded Variation Spaces with p-Variable." Mediterranean Journal of Mathematics 11, no. 4 (September 17, 2013): 1069–79. http://dx.doi.org/10.1007/s00009-013-0342-5.

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33

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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34

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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35

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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36

Drozdowski, Robert. "On the generalized variation and generalized weak variation of maps with values in metric linear spaces." Tatra Mountains Mathematical Publications 42, no. 1 (December 1, 2009): 131–48. http://dx.doi.org/10.2478/v10127-009-0013-x.

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Abstract In this paper, the class of maps (with values in a metric linear space) of a bounded generalized variation (bounded generalized weak variation) is described. Connections between those kinds of spaces are investigated.
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37

Marchena, B., and C. Piñeiro. "Bounded sets in the range of anX∗∗-valued measure with bounded variation." International Journal of Mathematics and Mathematical Sciences 23, no. 1 (2000): 21–30. http://dx.doi.org/10.1155/s0161171200001708.

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LetXbe a Banach space andA⊂Xan absolutely convex, closed, and bounded set. We give some sufficient and necessary conditions in order thatAlies in the range of a measure valued in the bidual spaceX∗∗and having bounded variation. Among other results, we prove thatX∗is a G. T.-space if and only ifAlies inside the range of someX∗∗-valued measure with bounded variation wheneverXAis isomorphic to a Hilbert space.
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38

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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39

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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40

Hencl, S. "Bilipschitz mappings with derivatives of bounded variation." Publicacions Matemàtiques 52 (January 1, 2008): 91–99. http://dx.doi.org/10.5565/publmat_52108_04.

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41

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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42

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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43

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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44

Bridges, Douglas, and Ayan Mahalanobis. "Bounded variation implies regulated: a constructive proof." Journal of Symbolic Logic 66, no. 4 (December 2001): 1695–700. http://dx.doi.org/10.2307/2694969.

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45

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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46

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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47

Castillo, René Erlin, Humberto Rafeiro, and Eduard Trousselot. "Embeddings on Spaces of Generalized Bounded Variation." Revista Colombiana de Matemáticas 48, no. 1 (June 26, 2014): 97–109. http://dx.doi.org/10.15446/recolma.v48n1.45197.

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48

Osher, Stanley, and Otmar Scherzer. "G-Norm Properties of Bounded Variation Regularization." Communications in Mathematical Sciences 2, no. 2 (2004): 237–54. http://dx.doi.org/10.4310/cms.2004.v2.n2.a6.

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49

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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50

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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