Wilker and Huygens- type inequalities for the generalized trigonometric and for the generalized hyperbolic functions
Wilker and Huygens-type inequalities for the generalized trigonometric and hyperbolic functions are established. Main results of this paper are proven with the aid of two inequalities which involve a few parameters. For special values of the parameters obtained results simplify to the known ones whi...
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| Veröffentlicht in: | Applied mathematics and computation Jg. 230; S. 211 - 217 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.03.2014
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | Wilker and Huygens-type inequalities for the generalized trigonometric and hyperbolic functions are established. Main results of this paper are proven with the aid of two inequalities which involve a few parameters. For special values of the parameters obtained results simplify to the known ones which are already published in mathematical literature. |
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| AbstractList | Wilker and Huygens-type inequalities for the generalized trigonometric and hyperbolic functions are established. Main results of this paper are proven with the aid of two inequalities which involve a few parameters. For special values of the parameters obtained results simplify to the known ones which are already published in mathematical literature. |
| Author | Neuman, Edward |
| Author_xml | – sequence: 1 givenname: Edward surname: Neuman fullname: Neuman, Edward email: edneuman76@gmail.com organization: Mathematical Research Institute, 144 Hawthorn Hollow, Carbondale, IL 62903, USA |
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| Cites_doi | 10.1080/10652460701284164 10.1016/j.jmaa.2013.07.021 10.1016/j.aml.2006.02.005 10.2307/4145099 10.1216/RMJ-2009-39-2-683 10.1016/j.aml.2007.09.001 10.1016/j.aml.2011.10.028 10.1080/10652460802340931 10.1080/10652460701712727 10.1080/10652469.2013.838761 10.1080/10652469.2012.684054 10.5486/PMD.2009.4530 10.1016/j.amc.2007.08.022 10.1016/j.aml.2006.05.022 |
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| References | Neuman (b0135) 2014; 25 Wu, Srivastava (b0110) 2008; 197 Sumner, Jagers, Vowe, Anglesio (b0060) 1991; 98 Guo, Qiao, Qi, Li (b0010) 2003; 6 Wu, Debnath (b0080) 2006; 19 Wu, Srivastava (b0100) 2007; 18 Zhu (b0125) 2007; 10 Wu, Baricz (b0075) 2009; 75 Wilker (b0065) 1989; 96 Zhu (b0120) 2005; 8 Klén, Vuorinen, Zhang (b0020) 2014; 409 Wu (b0070) 2009; 39 [math CA] 16 Apr 2011. Neuman (b0035) 2012; 24 Pinelis (b0055) 2004; 111 B.A. Bhayo, M. Vuorinen, Inequalities for eigenfunctions of the p-Laplacian, arXiv Wu, Debnath (b0090) 2008; 21 L. Zhu, Some new Wilker type inequalities for circular and hyperbolic functions, Abstract Appl. Anal. 2009 (2009), 9 pages, Article ID 485842. Wu, Debnath (b0085) 2007; 20 Wu, Srivastava (b0105) 2008; 19 Neuman, Sándor (b0050) 2010; 13 Wu, Debnath (b0095) 2012; 25 Neuman (b0030) 2012; 15 Lindqvist (b0025) 1995; 44 Neuman (b0040) 2013; 24 C. Huygens, Oeuvres Completes 1888–1940, Société Hollondaise des Science, Haga. Wu, Srivastava, Debnath (b0115) 2008; 19 Wu (10.1016/j.amc.2013.12.136_b0115) 2008; 19 Wu (10.1016/j.amc.2013.12.136_b0075) 2009; 75 Neuman (10.1016/j.amc.2013.12.136_b0030) 2012; 15 Klén (10.1016/j.amc.2013.12.136_b0020) 2014; 409 Wu (10.1016/j.amc.2013.12.136_b0095) 2012; 25 Wu (10.1016/j.amc.2013.12.136_b0090) 2008; 21 10.1016/j.amc.2013.12.136_b0140 Neuman (10.1016/j.amc.2013.12.136_b0040) 2013; 24 10.1016/j.amc.2013.12.136_b0015 Wilker (10.1016/j.amc.2013.12.136_b0065) 1989; 96 Wu (10.1016/j.amc.2013.12.136_b0080) 2006; 19 Zhu (10.1016/j.amc.2013.12.136_b0120) 2005; 8 Pinelis (10.1016/j.amc.2013.12.136_b0055) 2004; 111 Wu (10.1016/j.amc.2013.12.136_b0085) 2007; 20 Sumner (10.1016/j.amc.2013.12.136_b0060) 1991; 98 Neuman (10.1016/j.amc.2013.12.136_b0035) 2012; 24 10.1016/j.amc.2013.12.136_b0005 Guo (10.1016/j.amc.2013.12.136_b0010) 2003; 6 Neuman (10.1016/j.amc.2013.12.136_b0050) 2010; 13 Neuman (10.1016/j.amc.2013.12.136_b0135) 2014; 25 Wu (10.1016/j.amc.2013.12.136_b0110) 2008; 197 Wu (10.1016/j.amc.2013.12.136_b0100) 2007; 18 Zhu (10.1016/j.amc.2013.12.136_b0125) 2007; 10 Lindqvist (10.1016/j.amc.2013.12.136_b0025) 1995; 44 Wu (10.1016/j.amc.2013.12.136_b0070) 2009; 39 Wu (10.1016/j.amc.2013.12.136_b0105) 2008; 19 |
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| SubjectTerms | Computation Generalized hyperbolic functions Generalized trigonometric functions Hyperbolic functions Inequalities Mathematical analysis Mathematical models Wilker and Huygens- type inequalities |
| Title | Wilker and Huygens- type inequalities for the generalized trigonometric and for the generalized hyperbolic functions |
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