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Journal articles on the topic 'Isosceles orthogonality'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

He, Chan, and Dan Wang. "A Remark on the Homogeneity of Isosceles Orthogonality." Journal of Function Spaces 2014 (2014): 1–3. http://dx.doi.org/10.1155/2014/876015.

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Inspired by the definition of homogeneous direction of isosceles orthogonality, we introduce the notion of almost homogeneous direction of isosceles orthogonality and show that, surprisingly, these two notions coincide. Several known characterizations of inner products are improved.

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2

Mizuguchi, Hiroyasu. "The constants to measure the differences between Birkhoff and isosceles orthogonalities." Filomat 30, no. 10 (2016): 2761–70. http://dx.doi.org/10.2298/fil1610761m.

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The notion of orthogonality for vectors in inner product spaces is simple, interesting and fruitful. When moving to normed spaces, we have many possibilities to extend this notion. We consider Birkhoff orthogonality and isosceles orthogonality, which are the most used notions of orthogonality. In 2006, Ji and Wu introduced a geometric constant D(X) to give a quantitative characterization of the difference between these two orthogonality types. However, this constant was considered only in the unit sphere SX of the normed space X. In this paper, we introduce a new geometric constant IB(X) to measure the difference between Birkhoff and isosceles orthogonalities in the entire normed space X. To consider the difference between these orthogonalities, we also treat constant BI(X).

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3

Freese, Raymond, and Edward Andalafte. "Strong additivity of metric isosceles orthogonality." Journal of Geometry 62, no. 1-2 (July 1998): 121–28. http://dx.doi.org/10.1007/bf01237604.

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4

Alonso, Javier, Horst Martini, and Senlin Wu. "On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces." Aequationes mathematicae 83, no. 1-2 (September 18, 2011): 153–89. http://dx.doi.org/10.1007/s00010-011-0092-z.

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5

Ji, Donghai, and Senlin Wu. "Quantitative characterization of the difference between Birkhoff orthogonality and isosceles orthogonality." Journal of Mathematical Analysis and Applications 323, no. 1 (November 2006): 1–7. http://dx.doi.org/10.1016/j.jmaa.2005.10.004.

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6

Chmieliński, Jacek, and Paweł Wójcik. "Isosceles-orthogonality preserving property and its stability." Nonlinear Analysis: Theory, Methods & Applications 72, no. 3-4 (February 2010): 1445–53. http://dx.doi.org/10.1016/j.na.2009.08.028.

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7

Ojha, Bhuwan Prasad, and Prakash Muni Bajrayacharya. "Relation of Pythagorean and Isosceles Orthogonality with Best approximations in Normed Linear Space." Mathematics Education Forum Chitwan 4, no. 4 (November 15, 2019): 72–78. http://dx.doi.org/10.3126/mefc.v4i4.26360.

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In an arbitrary normed space, though the norm not necessarily coming from the inner product space, the notion of orthogonality may be introduced in various ways as suggested by the mathematicians like R.C. James, B.D. Roberts, G. Birkhoff and S.O. Carlsson. We aim to explore the application of orthogonality in normed linear spaces in the best approximation. Hence it has already been proved that Birkhoff orthogonality implies best approximation and best approximation implies Birkhoff orthogonality. Additionally, it has been proved that in the case of ε -orthogonality, ε -best approximation implies ε -orthogonality and vice-versa. In this article we established relation between Pythagorean orthogonality and best approximation as well as isosceles orthogonality and ε -best approximation in normed space.

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8

Ojha, Bhuwan Prasad, Prakash Muni Bajracharya, and Vishnu Narayan Mishra. "On Uniqueness of New Orthogonality via 2-HH Norm in Normed Linear Space." Journal of Function Spaces 2020 (November 20, 2020): 1–6. http://dx.doi.org/10.1155/2020/8835492.

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This paper generalizes the special case of the Carlsson orthogonality in terms of the 2-HH norm in real normed linear space. Dragomir and Kikianty (2010) proved in their paper that the Pythagorean orthogonality is unique in any normed linear space, and isosceles orthogonality is unique if and only if the space is strictly convex. This paper deals with the complete proof of the uniqueness of the new orthogonality through the medium of the 2-HH norm. We also proved that the Birkhoff and Robert orthogonality via the 2-HH norm are equivalent, whenever the underlying space is a real inner-product space.

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9

Kikianty, Eder, and Sever Dragomir. "On Carlsson type orthogonality and characterization of inner product spaces." Filomat 26, no. 4 (2012): 859–70. http://dx.doi.org/10.2298/fil1204859k.

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In an inner product space, two vectors are orthogonal if their inner product is zero. In a normed space, numerous notions of orthogonality have been introduced via equivalent propositions to the usual orthogonality, e.g. orthogonal vectors satisfy the Pythagorean law. In 2010, Kikianty and Dragomir [9] introduced the p-HH-norms (1 ? p < ?) on the Cartesian square of a normed space. Some notions of orthogonality have been introduced by utilizing the 2-HH-norm [10]. These notions of orthogonality are closely related to the classical Pythagorean orthogonality and Isosceles orthogonality. In this paper, a Carlsson type orthogonality in terms of the 2-HH-norm is considered, which generalizes the previous definitions. The main properties of this orthogonality are studied and some useful consequences are obtained. These consequences include characterizations of inner product space.

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10

Zamani, Ali, and Mohammad Sal Moslehian. "Approximate Roberts orthogonality sets and $${(\delta, \varepsilon)}$$ ( δ , ε ) -(a, b)-isosceles-orthogonality preserving mappings." Aequationes mathematicae 90, no. 3 (November 6, 2015): 647–59. http://dx.doi.org/10.1007/s00010-015-0383-x.

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11

Dadipour, F., F. Sadeghi, and A. Salemi. "Characterizations of inner product spaces involving homogeneity of isosceles orthogonality." Archiv der Mathematik 104, no. 5 (April 18, 2015): 431–39. http://dx.doi.org/10.1007/s00013-015-0762-5.

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12

Ji, Donghai, Jingying Li, and Senlin Wu. "On the Uniqueness of Isosceles Orthogonality in Normed Linear Spaces." Results in Mathematics 59, no. 1-2 (December 14, 2010): 157–62. http://dx.doi.org/10.1007/s00025-010-0069-6.

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13

Baronti, Marco, and Carlo Franchetti. "The isosceles orthogonality and a new 2-dimensional parameter in real normed spaces." Aequationes mathematicae 89, no. 3 (March 14, 2014): 673–83. http://dx.doi.org/10.1007/s00010-014-0255-9.

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14

Wu, Senlin, Yixia He, and Chan He. "Homogeneity of isosceles orthogonality, transitivity of the norm, and characterizations of inner product spaces." Aequationes mathematicae 95, no. 5 (August 9, 2021): 953–66. http://dx.doi.org/10.1007/s00010-021-00841-7.

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15

Hao, Cuixia, and Senlin Wu. "Homogeneity of isosceles orthogonality and related inequalities." Journal of Inequalities and Applications 2011, no. 1 (October 11, 2011). http://dx.doi.org/10.1186/1029-242x-2011-84.

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16

van Diejen, J. F., and E. Emsiz. "Cubature rules from Hall–Littlewood polynomials." IMA Journal of Numerical Analysis, May 21, 2020. http://dx.doi.org/10.1093/imanum/draa011.

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Abstract Discrete orthogonality relations for Hall–Littlewood polynomials are employed so as to derive cubature rules for the integration of homogeneous symmetric functions with respect to the density of the circular unitary ensemble (which originates from the Haar measure on the special unitary group $SU(n;\mathbb{C})$). By passing to Macdonald’s hyperoctahedral Hall–Littlewood polynomials, we moreover find analogous cubature rules for the integration with respect to the density of the circular quaternion ensemble (which originates in turn from the Haar measure on the compact symplectic group $Sp (n;\mathbb{H})$). The cubature formulas under consideration are exact for a class of rational symmetric functions with simple poles supported on a prescribed complex hyperplane arrangement. In the planar situations (corresponding to $SU(3;\mathbb{C})$ and $Sp (2;\mathbb{H})$), a determinantal expression for the Christoffel weights enables us to write down compact cubature rules for the integration over the equilateral triangle and the isosceles right triangle, respectively.

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