Relevant bibliographies by topics / Isosceles orthogonality

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  2. Dissertations / Theses

Academic literature on the topic 'Isosceles orthogonality'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Isosceles orthogonality"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Isosceles orthogonality"

1

Fankhänel, Andreas. "Metrical Problems in Minkowski Geometry." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-95007.

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In this dissertation we study basic metrical properties of 2-dimensional normed linear spaces, so-called (Minkowski or) normed planes. In the first chapter we introduce a notion of angular measure, and we investigate under what conditions certain angular measures in a Minkowski plane exist. We show that only the Euclidean angular measure has the property that in an isosceles triangle the base angles are of equal size. However, angular measures with the property that the angle between orthogonal vectors has a value of pi/2, i.e, a quarter of the full circle, exist in a wider variety of normed planes, depending on the type of orthogonality. Due to this we have a closer look at isosceles and Birkhoff orthogonality. Finally, we present results concerning angular bisectors. In the second chapter we pay attention to convex quadrilaterals. We give definitions of different types of rectangles and rhombi and analyse under what conditions they coincide. Combinations of defining properties of rectangles and rhombi will yield squares, and we will see that any two types of squares are equal if and only if the plane is Euclidean. Additionally, we define a ``new\'\' type of quadrilaterals, the so-called codises. Since codises and rectangles coincide in Radon planes, we will explain why it makes sense to distinguish these two notions. For this purpose we introduce the concept of associated parallelograms. Finally we will deal with metrically defined conics, i.e., with analogues of conic sections in normed planes. We define metric ellipses (hyperbolas) as loci of points that have constant sum (difference) of distances to two given points, the so-called foci. Also we define metric parabolas as loci of points whose distance to a given point equals the distance to a fixed line. We present connections between the shape of the unit ball B and the shape of conics. More precisely, we will see that straight segments and corner points of B cause, under certain conditions, that conics have straight segments and corner points, too. Afterwards we consider intersecting ellipses and hyperbolas with identical foci. We prove that in special Minkowski planes, namely in the subfamily of polygonal planes, confocal ellipses and hyperbolas intersect in a way called Birkhoff orthogonal, whenever the respective ellipse is large enough.
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Jahn, Thomas. "An Invitation to Generalized Minkowski Geometry." 2018. https://monarch.qucosa.de/id/qucosa%3A33435.

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The present thesis contributes to the theory of generalized Minkowski spaces as a continuation of Minkowski geometry, i.e., the geometry of finite-dimensional normed spaces over the field of real numbers. In a generalized Minkowski space, distance and length measurement is provided by a gauge, whose definition mimics the definition of a norm but lacks the symmetry requirement. This seemingly minor change in the definition is deliberately chosen. On the one hand, many techniques from Minkowski spaces can be adapted to generalized Minkowski spaces because several phenomena in Minkowski geometry simply do not depend on the symmetry of distance measurement. On the other hand, the possible asymmetry of the distance measurement set up by gauges is nonetheless meaningful and interesting for applications, e.g., in location science. In this spirit, the presentation of this thesis is led mainly by minimization problems from convex optimization and location science which are appealing to convex geometers, too. In addition, we study metrically defined objects, which may receive a new interpretation when we measure distances asymmetrically. To this end, we use a combination of methods from convex analysis and convex geometry to relate the properties of these objects to the shape of the unit ball of the generalized Minkowski space under consideration.
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