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Extension of Huygens type inequalities for Bessel and modified Bessel Functions

KHALED MEHREZ
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회논문집 (Communications of the KMS)|제34권 제3호|pp. 799-809|DOI 10.4134/CKMS.c180237

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참고문헌

키워드

the Bessel functionsthe modified Bessel functionsHuygens type inequalities
주제분류수학

초록

In this note our aim is to extend the Huygens type inequalities to the Bessel and modified Bessel functions of the first kind. Our main motivation to write this note is a recent publication of Zhu, which we wish to complement.

Abstract

In this note our aim is to extend the Huygens type inequalities to the Bessel and modified Bessel functions of the first kind. Our main motivation to write this note is a recent publication of Zhu, which we wish to complement.

참고문헌 (19)

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  3. Árpád Baricz, "Functional inequalities involving Bessel and modified Bessel functions of the first kind", Expositiones Mathematicae, 26(3), pp.279~293 (2008), Elsevier BV[DOI]
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  6. C. Huygens, "Oeuvres completes, publiees par la Societe hollandaise des science, 20 volumes" (1888)
  7. Khaled Mehrez, "Redheffer type inequalities for modified Bessel functions", Arab Journal of Mathematical Sciences, 22(1), pp.38~42 (2016), Elsevier BV[DOI]
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  9. K. Mehrez, "On monotonicity of ratios of some q-hypergeometric func-tions", Mat. Vesnik, 68(3), pp.225~231 (2016)
  10. Khaled Mehrez, "Functional Inequalities for the Mittag–Leffler Functions", Results in Mathematics, 72(1-2), pp.703~714 (2017), Springer Science and Business Media LLC[DOI]
  11. Edward Neuman, "On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities", Mathematical Inequalities & Applications, (4), pp.715~723 (1998), Element d.o.o.[DOI]
  12. Kottakkaran Sooppy Nisar, "Certain inequalities involving the k-Struve function", Journal of Inequalities and Applications, 2017(1) (2017), Springer Science and Business Media LLC[DOI]
  13. I. Pinelis, ""Non-strict" l'Hospital-type rules for monotonicity: intervals of constancy", JIPAM. J. Inequal. Pure Appl. Math, 8(1), pp.8~ (2007)
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  15. K. A. Selvakumaran, "Inclusion relationships for some subclasses of analytic functions associated with gener-alized Bessel functions", J. Comput. Anal. Appl, 24(1), pp.81~90 (2018)
  16. S. M. Sitnik, "Monotonicity of the ratios of some hypergeometric func-tions", Sib. Elektron. Mat. Izv, 13, pp.260~268 (2016)
  17. Sergei M. Sitnik, "Proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions", Analysis, 36(4) (2016), Walter de Gruyter GmbH[DOI]
  18. G. N. Watson, "A Treatise on the Theory of Bessel Functions" (1944), Cambridge University Press
  19. Ling Zhu, "Some new inequalities of the Huygens type", Computers & Mathematics with Applications, 58(6), pp.1180~1182 (2009), Elsevier BV[DOI]

관련 논문AI추천

Some inequalities and absolute monotonicity for modified Bessel functions of the first kindBai-Ni Guo, Feng Qi대한수학회 · 대한수학회논문집2016 · 제31권 제2호EXTENSION OF FRAME'S TYPE INEQUALITIES TO BESSEL AND MODIFIED BESSEL FUNCTIONSKHALED MEHREZ장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제4호Monotonicity properties of the Bessel-Struve kernelAnbhu Swaminathan, \'Arp\'ad Baricz, Saiful R. Mondal대한수학회 · 대한수학회보2016 · 제53권 제6호Bounds and inequalities of the modified Lommel functionsSaiful R. Mondal대한수학회 · 대한수학회논문집2019 · 제34권 제2호Tur\'an-type inequalities for Gauss and confluent hypergeometric functions via Cauchy-Bunyakovsky-Schwarz inequalityPiyush Kumar Bhandari, Sushil Kumar Bissu대한수학회 · 대한수학회논문집2018 · 제33권 제4호Redheffer type inequalities for the Fox-Wright functionsKHALED MEHREZ대한수학회 · 대한수학회논문집2019 · 제34권 제1호

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