Watanabe, Keiichi On a notion of complex Möbius gyrovector spaces. (English) Zbl 07523340 Nihonkai Math. J. 32, No. 2, 111-131 (2021). MSC: 46C05 20N05 46C99 46T99 51M10 83A05 PDF BibTeX XML Cite \textit{K. Watanabe}, Nihonkai Math. J. 32, No. 2, 111--131 (2021; Zbl 07523340) Full Text: Link OpenURL
Watanabe, Keiichi On Lipschitz continuity with respect to the Poincaré metric of linear contractions between Möbius gyrovector spaces. (English) Zbl 07465144 J. Inequal. Appl. 2021, Paper No. 166, 15 p. (2021). MSC: 47A30 20N05 46C05 46T99 51M10 83A05 PDF BibTeX XML Cite \textit{K. Watanabe}, J. Inequal. Appl. 2021, Paper No. 166, 15 p. (2021; Zbl 07465144) Full Text: DOI OpenURL
Demırel, Oğuzhan A characteristic of gyroisometries in Möbius gyrovector spaces. (English) Zbl 1459.51008 North-West. Eur. J. Math. 6, 107-118 (2020). Reviewer: Günter F. Steinke (Christchurch) MSC: 51M09 51M10 30F45 20N05 PDF BibTeX XML Cite \textit{O. Demırel}, North-West. Eur. J. Math. 6, 107--118 (2020; Zbl 1459.51008) Full Text: Link OpenURL
Watanabe, Keiichi Continuous quasi gyrolinear functionals on Möbius gyrovector spaces. (English) Zbl 1457.46029 J. Funct. Spaces 2020, Article ID 1950727, 14 p. (2020). MSC: 46C99 PDF BibTeX XML Cite \textit{K. Watanabe}, J. Funct. Spaces 2020, Article ID 1950727, 14 p. (2020; Zbl 1457.46029) Full Text: DOI OpenURL
Watanabe, Keiichi Cauchy-Bunyakovsky-Schwarz type inequalities related to Möbius operations. (English) Zbl 07459207 J. Inequal. Appl. 2019, Paper No. 179, 18 p. (2019). MSC: 46C05 20N05 26D20 46T99 51M10 83A05 PDF BibTeX XML Cite \textit{K. Watanabe}, J. Inequal. Appl. 2019, Paper No. 179, 18 p. (2019; Zbl 07459207) Full Text: DOI OpenURL
Watanabe, Keiichi A Cauchy-Bunyakovsky-Schwarz type inequality related to the Möbius addition. (English) Zbl 1412.46038 J. Math. Inequal. 12, No. 4, 989-996 (2018). MSC: 46C05 26D20 PDF BibTeX XML Cite \textit{K. Watanabe}, J. Math. Inequal. 12, No. 4, 989--996 (2018; Zbl 1412.46038) Full Text: DOI OpenURL
Demirel, Oğuzhan The first sharp gyrotriangle inequality in Möbius gyrovector space \((\mathbb D, \oplus, \otimes)\). (English) Zbl 1381.51018 Forum Geom. 17, 439-447 (2017). MSC: 51M99 51M16 PDF BibTeX XML Cite \textit{O. Demirel}, Forum Geom. 17, 439--447 (2017; Zbl 1381.51018) Full Text: Link OpenURL
Watanabe, Keiichi Orthogonal gyroexpansion in Möbius gyrovector spaces. (English) Zbl 1391.46032 J. Funct. Spaces 2017, Article ID 1518254, 13 p. (2017). MSC: 46C99 PDF BibTeX XML Cite \textit{K. Watanabe}, J. Funct. Spaces 2017, Article ID 1518254, 13 p. (2017; Zbl 1391.46032) Full Text: DOI OpenURL
Hatori, Osamu Examples and applications of generalized gyrovector spaces. (English) Zbl 1376.46056 Result. Math. 71, No. 1-2, 295-317 (2017). MSC: 46L99 PDF BibTeX XML Cite \textit{O. Hatori}, Result. Math. 71, No. 1--2, 295--317 (2017; Zbl 1376.46056) Full Text: DOI OpenURL
Abe, Toshikazu; Watanabe, Keiichi Finitely generated gyrovector subspaces and orthogonal gyrodecomposition in the Möbius gyrovector space. (English) Zbl 1357.15002 J. Math. Anal. Appl. 449, No. 1, 77-90 (2017). MSC: 15A03 51B10 PDF BibTeX XML Cite \textit{T. Abe} and \textit{K. Watanabe}, J. Math. Anal. Appl. 449, No. 1, 77--90 (2017; Zbl 1357.15002) Full Text: DOI OpenURL
Watanabe, Keiichi A confirmation by hand calculation that the Möbius ball is a gyrovector space. (English) Zbl 1382.51014 Nihonkai Math. J. 27, No. 1-2, 99-115 (2016). Reviewer: Victor V. Pambuccian (Phoenix) MSC: 51M10 20N05 46C99 51P05 PDF BibTeX XML Cite \textit{K. Watanabe}, Nihonkai Math. J. 27, No. 1--2, 99--115 (2016; Zbl 1382.51014) Full Text: Euclid OpenURL
Ungar, Abraham A. On the geometry induced by Lorentz transformations in pseudo-Euclidean spaces. (English) Zbl 1346.83006 Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 17th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 5–10, 2015. Sofia: Avangard Prima. 360-368 (2016). MSC: 83A05 15A63 20N02 20N05 22E10 83E15 PDF BibTeX XML Cite \textit{A. A. Ungar}, in: Proceedings of the 17th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 5--10, 2015. Sofia: Avangard Prima. 360--368 (2016; Zbl 1346.83006) Full Text: Euclid OpenURL
Abe, Toshikazu; Hatori, Osamu Generalized gyrovector spaces and a Mazur-Ulam theorem. (English) Zbl 1374.46026 Publ. Math. Debr. 87, No. 3-4, 393-413 (2015). Reviewer: Vladimir V. Peller (East Lansing) MSC: 46B99 20N05 PDF BibTeX XML Cite \textit{T. Abe} and \textit{O. Hatori}, Publ. Math. Debr. 87, No. 3--4, 393--413 (2015; Zbl 1374.46026) Full Text: DOI OpenURL
Kim, Sejong Distributivity on the gyrovector spaces. (English) Zbl 1384.20053 Kyungpook Math. J. 55, No. 1, 13-20 (2015). MSC: 20N05 51M10 81R05 PDF BibTeX XML Cite \textit{S. Kim}, Kyungpook Math. J. 55, No. 1, 13--20 (2015; Zbl 1384.20053) Full Text: DOI OpenURL
Ungar, Abraham Albert Analytic hyperbolic geometry in \(n\) dimensions. An introduction. (English) Zbl 1312.51001 Boca Raton, FL: CRC Press (ISBN 978-1-4822-3667-5/hbk; 978-1-4822-3668-2/ebook). xvii, 601 p. (2015). Reviewer: Rolf Riesinger (Wien) MSC: 51-01 51M10 51M09 51N25 51P05 83A05 20N05 PDF BibTeX XML Cite \textit{A. A. Ungar}, Analytic hyperbolic geometry in \(n\) dimensions. An introduction. Boca Raton, FL: CRC Press (2015; Zbl 1312.51001) Full Text: Link OpenURL
Ungar, Abraham Albert On the study of hyperbolic triangles and circles by hyperbolic barycentric coordinates in relativistic hyperbolic geometry. (English) Zbl 1323.30059 Rassias, Themistocles M. (ed.) et al., Mathematics without boundaries. Surveys in pure mathematics. New York, NY: Springer (ISBN 978-1-4939-1105-9/hbk; 978-1-4939-1106-6/ebook). 569-649 (2014). Reviewer: Athanase Papadopoulos (Strasbourg) MSC: 30F45 PDF BibTeX XML Cite \textit{A. A. Ungar}, in: Mathematics without boundaries. Surveys in pure mathematics. New York, NY: Springer. 569--649 (2014; Zbl 1323.30059) Full Text: DOI arXiv OpenURL
Ungar, Abraham Albert An introduction to hyperbolic barycentric coordinates and their applications. (English) Zbl 1317.51018 Pardalos, Panos M. (ed.) et al., Mathematics without boundaries. Surveys in interdisciplinary research. New York, NY: Springer (ISBN 978-1-4939-1123-3/hbk; 978-1-4939-1124-0/ebook). 577-648 (2014). Reviewer: Mikhail Belolipetsky (Rio de Janeiro) MSC: 51M10 PDF BibTeX XML Cite \textit{A. A. Ungar}, in: Mathematics without boundaries. Surveys in interdisciplinary research. New York, NY: Springer. 577--648 (2014; Zbl 1317.51018) Full Text: DOI arXiv OpenURL
Urribarri, Dana K.; Castro, Silvia M.; Martig, Sergio R. Gyrolayout: a hyperbolic level-of-detail tree layout. (English) Zbl 1412.68288 J. UCS 19, No. 1, 132-156 (2013). MSC: 68U05 68P99 PDF BibTeX XML Cite \textit{D. K. Urribarri} et al., J. UCS 19, No. 1, 132--156 (2013; Zbl 1412.68288) Full Text: Link OpenURL
Andrica, Dorin; Barbu, Cătălin The hyperbolic Desargues theorem in the Poincaré model of hyperbolic geometry. (English) Zbl 1313.30156 Stud. Univ. Babeș-Bolyai, Math. 58, No. 4, 431-435 (2013). MSC: 30F45 20N99 51B10 51M10 PDF BibTeX XML Cite \textit{D. Andrica} and \textit{C. Barbu}, Stud. Univ. Babeș-Bolyai, Math. 58, No. 4, 431--435 (2013; Zbl 1313.30156) OpenURL
Sönmez, Nilgün; Ungar, A. A. The Einstein relativistic velocity model of hyperbolic geometry and its plane separation axiom. (English) Zbl 1266.51026 Adv. Appl. Clifford Algebr. 23, No. 1, 209-236 (2013). MSC: 51M10 83A05 51M05 PDF BibTeX XML Cite \textit{N. Sönmez} and \textit{A. A. Ungar}, Adv. Appl. Clifford Algebr. 23, No. 1, 209--236 (2013; Zbl 1266.51026) Full Text: DOI OpenURL
Demirel, Oğuzhan; Seyrantepe, Emine Soytürk The cogyrolines of Möbius gyrovector spaces are metric but not periodic. (English) Zbl 1269.39007 Aequationes Math. 85, No. 1-2, 185-200 (2013). Reviewer: Prasanna Sahoo (Louisville) MSC: 39B42 51M05 51M10 51M25 54E35 51B10 PDF BibTeX XML Cite \textit{O. Demirel} and \textit{E. S. Seyrantepe}, Aequationes Math. 85, No. 1--2, 185--200 (2013; Zbl 1269.39007) Full Text: DOI OpenURL
Demirel, O.; Soytürk Seyrantepe, E.; Sönmez, N. Metric and periodic lines in the Poincaré ball model of hyperbolic geometry. (English) Zbl 1367.51019 Bull. Iran. Math. Soc. 38, No. 3, 805-815 (2012). Reviewer: Abraham A. Ungar (Fargo) (MR 3028471) MSC: 51M10 51F99 PDF BibTeX XML Cite \textit{O. Demirel} et al., Bull. Iran. Math. Soc. 38, No. 3, 805--815 (2012; Zbl 1367.51019) OpenURL
Barbu, Cătălin; Pişcoran, Laurian-Ioan The orthopole theorem in the Poincaré disc model of hyperbolic geometry. (English) Zbl 1286.51011 Acta Univ. Sapientiae, Math. 4, No. 1, 20-25 (2012). Reviewer: Francisco Vittone (Rosario) MSC: 51M10 51K05 PDF BibTeX XML Cite \textit{C. Barbu} and \textit{L.-I. Pişcoran}, Acta Univ. Sapientiae, Math. 4, No. 1, 20--25 (2012; Zbl 1286.51011) OpenURL
Barbu, Cătălin; Smarandache, Florentin A new proof of Menelaus’s theorem of hyperbolic quadrilaterals in the Poincaré model of hyperbolic geometry. (English) Zbl 1272.51010 Int. J. Math. Comb. 2012, No. 3, 118-123 (2012). Reviewer: Shing So (Warrensburg) MSC: 51M10 51K05 PDF BibTeX XML Cite \textit{C. Barbu} and \textit{F. Smarandache}, Int. J. Math. Comb. 2012, No. 3, 118--123 (2012; Zbl 1272.51010) Full Text: arXiv OpenURL
Barbu, Cătălin; Pişcoran, Laurian-Ioan Some hyperbolic concurrency results in the Poincaré disc. (English) Zbl 1265.30185 Carpathian J. Math. 28, No. 1, 9-15 (2012). MSC: 30F45 PDF BibTeX XML Cite \textit{C. Barbu} and \textit{L.-I. Pişcoran}, Carpathian J. Math. 28, No. 1, 9--15 (2012; Zbl 1265.30185) OpenURL
Barbu, Cătălin; Pişcoran, Laurian-Ioan Gülicher’ theorem in the Poincaré disc model of hyperbolic geometry. (English) Zbl 1308.51013 Math. Aeterna 1, No. 5, 305-311 (2011). MSC: 51K05 51M10 30F45 20N99 51B10 PDF BibTeX XML Cite \textit{C. Barbu} and \textit{L.-I. Pişcoran}, Math. Æterna 1, No. 5, 305--311 (2011; Zbl 1308.51013) OpenURL
Demirel, Oğuzhan; Soytürk Seyrantepe, Emine The theorems of Urquhart and Steiner-Lehmus in the Poincaré ball model of hyperbolic geometry. (English) Zbl 1289.51001 Mat. Vesn. 63, No. 4, 263-274 (2011). Reviewer: Milica Stojanović (Beograd) MSC: 51B10 51M10 PDF BibTeX XML Cite \textit{O. Demirel} and \textit{E. Soytürk Seyrantepe}, Mat. Vesn. 63, No. 4, 263--274 (2011; Zbl 1289.51001) OpenURL
Barbu, Cătălin The hyperbolic Stewart theorem in the Einstein relativistic velocity model of hyperbolic geometry. (English) Zbl 1249.51008 An. Univ. Oradea, Fasc. Mat. 18, 133-138 (2011). MSC: 51M10 51K05 30F45 20N99 51B10 PDF BibTeX XML Cite \textit{C. Barbu}, An. Univ. Oradea, Fasc. Mat. 18, 133--138 (2011; Zbl 1249.51008) OpenURL
Pişcoran, Laurian-Ioan; Barbu, Cătălin Pappus’s harmonic theorem in the Einstein relativistic velocity model of hyperbolic geometry. (English) Zbl 1240.51006 Stud. Univ. Babeș-Bolyai, Math. 56, No. 1, 101-107 (2011). MSC: 51K05 51M10 30F45 20N99 51B10 PDF BibTeX XML Cite \textit{L.-I. Pişcoran} and \textit{C. Barbu}, Stud. Univ. Babeș-Bolyai, Math. 56, No. 1, 101--107 (2011; Zbl 1240.51006) OpenURL
Barbu, Cătălin Trigonometric proof of Steiner-Lehmus theorem in hyperbolic geometry. (English) Zbl 1265.30184 Acta Univ. Apulensis, Math. Inform. 23, 63-67 (2010). Reviewer: Mowaffaq Hajja (Amman) MSC: 30F45 51B10 51M10 PDF BibTeX XML Cite \textit{C. Barbu}, Acta Univ. Apulensis, Math. Inform. 23, 63--67 (2010; Zbl 1265.30184) OpenURL
Barbu, Cătălin The isotomic transversal theorem and the Neuberg’s theorem in the Poincaré model of hyperbolic geometry. (English) Zbl 1265.51012 Sci. Stud. Res., Ser. Math. Inform. 20, No. 1, 37-44 (2010). MSC: 51M10 51K05 PDF BibTeX XML Cite \textit{C. Barbu}, Sci. Stud. Res., Ser. Math. Inform. 20, No. 1, 37--44 (2010; Zbl 1265.51012) OpenURL
Demirel, O. The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry. (English) Zbl 1212.51002 Commentat. Math. Univ. Carol. 50, No. 3, 359-371 (2009). MSC: 51B10 51M10 30F45 20N05 PDF BibTeX XML Cite \textit{O. Demirel}, Commentat. Math. Univ. Carol. 50, No. 3, 359--371 (2009; Zbl 1212.51002) Full Text: EuDML EMIS OpenURL
Ungar, Abraham Albert A gyrovector space approach to hyperbolic geometry. (English) Zbl 1208.51014 Synthesis Lectures on Mathematics and Statistics 4. San Rafael, CA: Morgan & Claypool Publishers (ISBN 978-1-59829-822-2/pbk; 978-1-59829-823-9/ebook). xii, 182 p. (2009). Reviewer: Victor V. Pambuccian (Phoenix) MSC: 51M10 51-01 PDF BibTeX XML Cite \textit{A. A. Ungar}, A gyrovector space approach to hyperbolic geometry. San Rafael, CA: Morgan \& Claypool Publishers (2009; Zbl 1208.51014) Full Text: DOI OpenURL
Ungar, Abraham A. Hyperbolic barycentric coordinates. (English) Zbl 1181.51015 Aust. J. Math. Anal. Appl. 6, No. 1, Article 18, 35 p. (2009). Reviewer: Andrzej Szczepański (Gdańsk) MSC: 51M10 83A05 51B10 51P05 51B20 51M20 PDF BibTeX XML Cite \textit{A. A. Ungar}, Aust. J. Math. Anal. Appl. 6, No. 1, Article 18, 35 p. (2009; Zbl 1181.51015) Full Text: Link OpenURL
Ungar, Abraham A. Möbius gyrovector spaces in quantum information and computation. (English) Zbl 1212.51013 Commentat. Math. Univ. Carol. 49, No. 2, 341-356 (2008). MSC: 51M10 51P05 81P15 PDF BibTeX XML Cite \textit{A. A. Ungar}, Commentat. Math. Univ. Carol. 49, No. 2, 341--356 (2008; Zbl 1212.51013) Full Text: EuDML EMIS OpenURL
Ungar, Abraham Albert Analytic hyperbolic geometry and Albert Einstein’s special theory of relativity. (English) Zbl 1147.83004 Hackensack, NJ: World Scientific (ISBN 978-981-277-229-9/hbk). xix, 628 p. (2008). Reviewer: Hans-Jürgen Schmidt (Potsdam) MSC: 83-02 01A60 51P05 83A05 83C10 85A05 74H40 PDF BibTeX XML Cite \textit{A. A. Ungar}, Analytic hyperbolic geometry and Albert Einstein's special theory of relativity. Hackensack, NJ: World Scientific (2008; Zbl 1147.83004) OpenURL
Ungar, Abraham A. The hyperbolic square and Möbius transformations. (English) Zbl 1129.30027 Banach J. Math. Anal. 1, No. 1, 101-116 (2007). MSC: 30F45 20N05 PDF BibTeX XML Cite \textit{A. A. Ungar}, Banach J. Math. Anal. 1, No. 1, 101--116 (2007; Zbl 1129.30027) Full Text: DOI EuDML EMIS OpenURL
Ungar, Abraham A. Gyrovector spaces and their differential geometry. (English) Zbl 1147.51010 Nonlinear Funct. Anal. Appl. 10, No. 5, 791-834 (2005). Reviewer: Norbert Knarr (Gießen) MSC: 51H25 83A05 20N05 53A99 PDF BibTeX XML Cite \textit{A. A. Ungar}, Nonlinear Funct. Anal. Appl. 10, No. 5, 791--834 (2005; Zbl 1147.51010) OpenURL
Ungar, A. A. Einstein’s special relativity: Unleashing the power of its hyperbolic geometry. (English) Zbl 1071.83505 Comput. Math. Appl. 49, No. 2-3, 187-221 (2005). MSC: 83A05 83E05 PDF BibTeX XML Cite \textit{A. A. Ungar}, Comput. Math. Appl. 49, No. 2--3, 187--221 (2005; Zbl 1071.83505) Full Text: DOI OpenURL
Ungar, Abraham A. The hyperbolic triangle centroid. (English) Zbl 1099.51008 Commentat. Math. Univ. Carol. 45, No. 2, 355-369 (2004). Reviewer: Alena Vanžurová (Olomouc) MSC: 51P05 51M10 83A05 20N05 PDF BibTeX XML Cite \textit{A. A. Ungar}, Commentat. Math. Univ. Carol. 45, No. 2, 355--369 (2004; Zbl 1099.51008) Full Text: EuDML EMIS OpenURL
Kasparian, Azniv; Ungar, Abraham A. Lie gyrovector spaces. (English) Zbl 1071.83001 J. Geom. Symmetry Phys. 1, 3-53 (2004). Reviewer: Neculai Papaghiuc (Iaşi) MSC: 83A05 53C30 53B30 PDF BibTeX XML Cite \textit{A. Kasparian} and \textit{A. A. Ungar}, J. Geom. Symmetry Phys. 1, 3--53 (2004; Zbl 1071.83001) Full Text: Link OpenURL
Ungar, Abraham A. Beyond the Einstein addition law and its gyroscopic Thomas precession. The theory of gyrogroups and gyrovector spaces. (English) Zbl 0972.83002 Fundamental Theories of Physics. 117. Dordrecht: Kluwer Academic Publishers. xlii, 413 p. (2001). Reviewer: Hans-Jürgen Schmidt (Potsdam) MSC: 83-02 83A05 51P05 83C10 53C50 PDF BibTeX XML Cite \textit{A. A. Ungar}, Beyond the Einstein addition law and its gyroscopic Thomas precession. The theory of gyrogroups and gyrovector spaces. Dordrecht: Kluwer Academic Publishers (2001; Zbl 0972.83002) OpenURL
Birman, Graciela S.; Ungar, Abraham A. The hyperbolic derivative in the Poincaré ball model of hyperbolic geometry. (English) Zbl 0976.51009 J. Math. Anal. Appl. 254, No. 1, 321-333 (2001). Reviewer: V.V.Chueshev (Kemerovo) MSC: 51M10 20N05 53C22 PDF BibTeX XML Cite \textit{G. S. Birman} and \textit{A. A. Ungar}, J. Math. Anal. Appl. 254, No. 1, 321--333 (2001; Zbl 0976.51009) Full Text: DOI Link OpenURL
Ungar, Abraham A. Gyrovector spaces in the service of hyperbolic geometry. (English) Zbl 0978.20040 Rassias, Themistocles M. (ed.), Mathematical analysis and applications. Palm Harbour, FL: Hadronic Press. 305-360 (2000). Reviewer: C.Pereira da Silva (Curitiba) MSC: 20N05 51M10 51P05 PDF BibTeX XML Cite \textit{A. A. Ungar}, in: Mathematical analysis and applications. Palm Harbour, FL: Hadronic Press. 305--360 (2000; Zbl 0978.20040) OpenURL
Ungar, A. A. Hyperbolic trigonometry in the Einstein relativistic velocity model of hyperbolic geometry. (English) Zbl 0965.83004 Comput. Math. Appl. 40, No. 2-3, 313-332 (2000). Reviewer: Trandafir Balan (Craiova) MSC: 83A05 51P05 83C10 51M10 PDF BibTeX XML Cite \textit{A. A. Ungar}, Comput. Math. Appl. 40, No. 2--3, 313--332 (2000; Zbl 0965.83004) Full Text: DOI OpenURL