메뉴 건너뛰기




Volumn 59, Issue 2, 2010, Pages 724-736

Jordan type inequalities involving the Bessel and modified Bessel functions

Author keywords

Bessel, modified Bessel, spherical Bessel and modified spherical Bessel functions; Best constant; General forms of Jordan type double inequalities; Lower and upper bounds; New infinite series for the Bessel and modified Bessel functions

Indexed keywords

BEST CONSTANTS; INFINITE SERIES; LOWER AND UPPER BOUNDS; MODIFIED BESSEL FUNCTION; NEW INFINITE SERIES FOR THE BESSEL AND MODIFIED BESSEL FUNCTIONS;

EID: 72949121902     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.10.020     Document Type: Article
Times cited : (13)

References (43)
  • 2
    • 27844473787 scopus 로고    scopus 로고
    • Jordan's inequality
    • Feng Y.F. Jordan's inequality. Math. Mag. 69 (1996) 126-127
    • (1996) Math. Mag. , vol.69 , pp. 126-127
    • Feng, Y.F.1
  • 4
    • 0000976145 scopus 로고    scopus 로고
    • Some inequalities constructed by Tchebysheff's integral inequality
    • Qi F., Cui L.-H., and Xu S.-L. Some inequalities constructed by Tchebysheff's integral inequality. Math. Inequal. Appl. 4 (1999) 517-528
    • (1999) Math. Inequal. Appl. , vol.4 , pp. 517-528
    • Qi, F.1    Cui, L.-H.2    Xu, S.-L.3
  • 5
    • 27844512467 scopus 로고    scopus 로고
    • A new refined form of Jordan's inequality and its applications
    • Özban A.Y. A new refined form of Jordan's inequality and its applications. Appl. Math. Lett. 19 (2006) 155-160
    • (2006) Appl. Math. Lett. , vol.19 , pp. 155-160
    • Özban, A.Y.1
  • 6
    • 29144504125 scopus 로고    scopus 로고
    • Sharpening Jordan's inequality and Yang Le inequality
    • Zhu L. Sharpening Jordan's inequality and Yang Le inequality. Appl. Math. Lett. 19 (2006) 240-243
    • (2006) Appl. Math. Lett. , vol.19 , pp. 240-243
    • Zhu, L.1
  • 7
    • 33744919530 scopus 로고    scopus 로고
    • Sharpening Jordan's inequality and Yang Le inequality, II
    • Zhu L. Sharpening Jordan's inequality and Yang Le inequality, II. Appl. Math. Lett. 19 (2006) 990-994
    • (2006) Appl. Math. Lett. , vol.19 , pp. 990-994
    • Zhu, L.1
  • 8
    • 33644546075 scopus 로고    scopus 로고
    • Sharpening of Jordan's inequalities and its applications
    • Zhu L. Sharpening of Jordan's inequalities and its applications. Math. Inequal. Appl. 9 (2006) 103-106
    • (2006) Math. Inequal. Appl. , vol.9 , pp. 103-106
    • Zhu, L.1
  • 9
    • 41949093839 scopus 로고    scopus 로고
    • A general refinement of Jordan type inequality
    • Zhu L. A general refinement of Jordan type inequality. Comput. Math. Appl. 55 (2008) 2498-2505
    • (2008) Comput. Math. Appl. , vol.55 , pp. 2498-2505
    • Zhu, L.1
  • 10
    • 55349144182 scopus 로고    scopus 로고
    • A general form of Jordan's inequality and its applications
    • Zhu L. A general form of Jordan's inequality and its applications. Math. Inequal. Appl. 11 4 (2008) 655-665
    • (2008) Math. Inequal. Appl. , vol.11 , Issue.4 , pp. 655-665
    • Zhu, L.1
  • 11
    • 56949096383 scopus 로고    scopus 로고
    • General forms of Jordan and Yang Le inequalities
    • Zhu L. General forms of Jordan and Yang Le inequalities. Appl. Math. Lett. 22 (2009) 236-241
    • (2009) Appl. Math. Lett. , vol.22 , pp. 236-241
    • Zhu, L.1
  • 12
    • 84867921649 scopus 로고    scopus 로고
    • New strengthened Jordan's inequality and its applications
    • Debnath L., and Zhao C.J. New strengthened Jordan's inequality and its applications. Appl. Math. Lett. 16 4 (2003) 557-560
    • (2003) Appl. Math. Lett. , vol.16 , Issue.4 , pp. 557-560
    • Debnath, L.1    Zhao, C.J.2
  • 13
    • 27844521401 scopus 로고    scopus 로고
    • Generalization and strengthen of Yang Le inequality
    • (in Chinese)
    • Zhao C.J. Generalization and strengthen of Yang Le inequality. Math. Practice Theory 4 (2000) 493-497 (in Chinese)
    • (2000) Math. Practice Theory , vol.4 , pp. 493-497
    • Zhao, C.J.1
  • 14
    • 33748322496 scopus 로고    scopus 로고
    • On generalizations and refinements of Jordan type inequality
    • Wu S.H. On generalizations and refinements of Jordan type inequality. Octogon Math. Mag. 12 1 (2004) 267-272
    • (2004) Octogon Math. Mag. , vol.12 , Issue.1 , pp. 267-272
    • Wu, S.H.1
  • 15
    • 33748307470 scopus 로고    scopus 로고
    • A new generalized and sharp version of Jordan's inequality and its applications to the improvement of the Yang Le inequality
    • Wu S.H., and Debnath L. A new generalized and sharp version of Jordan's inequality and its applications to the improvement of the Yang Le inequality. Appl. Math. Lett. 19 (2006) 1378-1384
    • (2006) Appl. Math. Lett. , vol.19 , pp. 1378-1384
    • Wu, S.H.1    Debnath, L.2
  • 16
    • 33845347537 scopus 로고    scopus 로고
    • A new generalized and sharp version of Jordan's inequality and its applications to the improvement of the Yang Le inequality, II
    • Wu S.H., and Debnath L. A new generalized and sharp version of Jordan's inequality and its applications to the improvement of the Yang Le inequality, II. Appl. Math. Lett. 20 (2007) 1414-1417
    • (2007) Appl. Math. Lett. , vol.20 , pp. 1414-1417
    • Wu, S.H.1    Debnath, L.2
  • 17
    • 45049084883 scopus 로고    scopus 로고
    • Jordan-type inequalities for differentiable functions and their applications
    • Wu S.H., and Debnath L. Jordan-type inequalities for differentiable functions and their applications. Appl. Math. Lett. 21 (2008) 803-809
    • (2008) Appl. Math. Lett. , vol.21 , pp. 803-809
    • Wu, S.H.1    Debnath, L.2
  • 18
    • 39449088258 scopus 로고    scopus 로고
    • A further refinement of a Jordan type inequality and its application
    • Wu S.H., and Srivastava H.M. A further refinement of a Jordan type inequality and its application. Appl. Math. Comput. 197 (2008) 914-923
    • (2008) Appl. Math. Comput. , vol.197 , pp. 914-923
    • Wu, S.H.1    Srivastava, H.M.2
  • 19
    • 44149106505 scopus 로고    scopus 로고
    • On the concavity of frac(sin x, x)
    • Sándor J. On the concavity of frac(sin x, x). Octogon Math. Mag. 13 1 (2005) 406-407
    • (2005) Octogon Math. Mag. , vol.13 , Issue.1 , pp. 406-407
    • Sándor, J.1
  • 20
    • 33947630325 scopus 로고    scopus 로고
    • An identity related to Jordan's inequality
    • Article ID 76782, 6 pages. Available online at: http://dx.doi.org/10.1155/IJMMS/2006/76782
    • Li J.-L. An identity related to Jordan's inequality. Intern. J. Math. Math. Sci. 2006 (2006). http://dx.doi.org/10.1155/IJMMS/2006/76782 Article ID 76782, 6 pages. Available online at: http://dx.doi.org/10.1155/IJMMS/2006/76782
    • (2006) Intern. J. Math. Math. Sci. , vol.2006
    • Li, J.-L.1
  • 21
    • 41149117516 scopus 로고    scopus 로고
    • On the strengthened Jordan's inequality
    • Article ID 74328, 8 pages. Available online at: http://dx.doi.org/10.1155/2007/74328
    • Li J.L., and Li Y.L. On the strengthened Jordan's inequality. J. Inequal. Appl. Volume 2007 (2007). http://dx.doi.org/10.1155/2007/74328 Article ID 74328, 8 pages. Available online at: http://dx.doi.org/10.1155/2007/74328
    • (2007) J. Inequal. Appl. , vol.2007
    • Li, J.L.1    Li, Y.L.2
  • 22
    • 35649005027 scopus 로고    scopus 로고
    • Some inequalities involving generalized Bessel functions
    • Baricz Á. Some inequalities involving generalized Bessel functions. Math. Ineq. Appl. 10 (2007) 827-842
    • (2007) Math. Ineq. Appl. , vol.10 , pp. 827-842
    • Baricz, Á.1
  • 23
    • 72949111910 scopus 로고    scopus 로고
    • Á. Baricz, Generalized Bessel functions of the First Kind, Ph.D. Thesis, Babes-Bolyai University, 2008
    • Á. Baricz, Generalized Bessel functions of the First Kind, Ph.D. Thesis, Babes-Bolyai University, 2008
  • 24
    • 46849085625 scopus 로고    scopus 로고
    • Jordan-type inequalities for generalized Bessel functions
    • art. 39
    • Baricz Á. Jordan-type inequalities for generalized Bessel functions. J. Inequal. Pure Appl. Math. 9 2 (2008) art. 39
    • (2008) J. Inequal. Pure Appl. Math. , vol.9 , Issue.2
    • Baricz, Á.1
  • 25
    • 61649122387 scopus 로고    scopus 로고
    • Sharp Jordan-type inequalities for Bessel functions
    • Baricz Á., and Wu S.H. Sharp Jordan-type inequalities for Bessel functions. Publ. Math. Debrecen 74 (2009) 107-126
    • (2009) Publ. Math. Debrecen , vol.74 , pp. 107-126
    • Baricz, Á.1    Wu, S.H.2
  • 26
    • 27844525601 scopus 로고    scopus 로고
    • Inequalities involving generalized Bessel functions
    • art.126
    • Baricz Á., and Neuman E. Inequalities involving generalized Bessel functions. J. Inequal. Pure Appl. Math. 6 4 (2005) art.126
    • (2005) J. Inequal. Pure Appl. Math. , vol.6 , Issue.4
    • Baricz, Á.1    Neuman, E.2
  • 27
    • 40749115091 scopus 로고    scopus 로고
    • Thesis supervised by Professor Feng Qi and submitted for the Master Degree of Science at Henan Polytechnic University in June, in Chinese
    • D.-W. Niu, Generalizations of Jordan's inequality and applications, Thesis supervised by Professor Feng Qi and submitted for the Master Degree of Science at Henan Polytechnic University in June 2007. (2007) (in Chinese)
    • (2007) Generalizations of Jordan's inequality and applications
    • Niu, D.-W.1
  • 28
    • 40749147264 scopus 로고    scopus 로고
    • A general refinement of Jordan's inequality and a refinement of L. Yang's inequality
    • Niu D.-W., Huo Zh.-H., Cao J., and Qi F. A general refinement of Jordan's inequality and a refinement of L. Yang's inequality. Integral Transforms Spec. Funct. 19 3 (2008) 157-164
    • (2008) Integral Transforms Spec. Funct. , vol.19 , Issue.3 , pp. 157-164
    • Niu, D.-W.1    Huo, Zh.-H.2    Cao, J.3    Qi, F.4
  • 29
    • 61649103502 scopus 로고    scopus 로고
    • Refinements, generalizations and applications of Jordan's inequality and related problems
    • art. 9
    • Qi F., and Niu D.-W. Refinements, generalizations and applications of Jordan's inequality and related problems. RGMIA Res. Rep. Coll. 11 2 (2008) art. 9
    • (2008) RGMIA Res. Rep. Coll. , vol.11 , Issue.2
    • Qi, F.1    Niu, D.-W.2
  • 32
    • 46149122293 scopus 로고    scopus 로고
    • Functional inequalities involving Bessel and modified Bessel functions of the first kind
    • Baricz Á. Functional inequalities involving Bessel and modified Bessel functions of the first kind. Expo. Math. 26 3 (2008) 279-293
    • (2008) Expo. Math. , vol.26 , Issue.3 , pp. 279-293
    • Baricz, Á.1
  • 33
    • 34247136901 scopus 로고    scopus 로고
    • Landen-type inequality for Bessel functions
    • Baricz Á. Landen-type inequality for Bessel functions. Comput. Methods Funct. Theory 5 (2005) 373-379
    • (2005) Comput. Methods Funct. Theory , vol.5 , pp. 373-379
    • Baricz, Á.1
  • 34
    • 33646076444 scopus 로고    scopus 로고
    • Functional inequalities involving special functions
    • Baricz Á. Functional inequalities involving special functions. J. Math. Anal. Appl. 319 (2006) 450-459
    • (2006) J. Math. Anal. Appl. , vol.319 , pp. 450-459
    • Baricz, Á.1
  • 35
    • 33750984512 scopus 로고    scopus 로고
    • Functional inequalities involving special functions II
    • Baricz Á. Functional inequalities involving special functions II. J. Math. Anal. Appl. 327 (2007) 1202-1213
    • (2007) J. Math. Anal. Appl. , vol.327 , pp. 1202-1213
    • Baricz, Á.1
  • 41
    • 0031251626 scopus 로고    scopus 로고
    • A code to evaluate modified Bessel functions based on the continued fraction method
    • Segura J., Fernfindez de Cordoba P., and Ratis Yu.L. A code to evaluate modified Bessel functions based on the continued fraction method. Comput. Phys. Commun. 105 (1997) 263-272
    • (1997) Comput. Phys. Commun. , vol.105 , pp. 263-272
    • Segura, J.1    Fernfindez de Cordoba, P.2    Ratis, Yu.L.3
  • 43
    • 50049113000 scopus 로고    scopus 로고
    • Geometric properties of generalized Bessel functions
    • Baricz Á. Geometric properties of generalized Bessel functions. Publ. Math. Debrecen 73 (2008) 155-178
    • (2008) Publ. Math. Debrecen , vol.73 , pp. 155-178
    • Baricz, Á.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.