Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-20T04:01:34.367Z Has data issue: false hasContentIssue false
  • English
  • Français

Functional inequalities for modified Struve functions

Published online by Cambridge University Press:  03 October 2014

Árpád Baricz  and
Tibor K. Pogány
Árpád Baricz
Affiliation:
Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania Institute of Applied Mathematics, John von Neumann Faculty of Informatics, Óbuda University, 1034 Budapest, Hungary, (bariczocsi@yahoo.com)
Tibor K. Pogány
Affiliation:
Faculty of Maritime Studies, University of Rijeka, 51000 Rijeka, Croatia Institute of Applied Mathematics, John von Neumann Faculty of Informatics, Óbuda University, 1034 Budapest, Hungary, (poganj@brod.pfri.hr)
Get access Rights & Permissions [Opens in a new window]

Abstract

By using a general result on the monotonicity of quotients of power series, our aim is to prove some monotonicity and convexity results for the modified Struve functions. Moreover, as consequences of the above-mentioned results, we present some functional inequalities as well as lower and upper bounds for modified Struve functions. Our main results complement and improve the 1998 results of Joshi and Nalwaya.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 5 , October 2014 , pp. 891 - 904
Copyright
Copyright © Royal Society of Edinburgh 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Alzer, H. and Qiu, S.-L.. Monotonicity theorems and inequalities for the complete elliptic integrals. J. Computat. Appl. Math. 172 (2004), 289–312.Google Scholar
2Anderson, G. D., Vamanamurthy, M. K. and Vuorinen, M.. Generalized convexity and inequalities. J. Math. Analysis Applic. 335 (2007), 1294–1308.Google Scholar
3Balasubramanian, R., Ponnusamy, S. and Vuorinen, M.. Functional inequalities for the quotients of hypergeometric functions. J. Math. Analysis Applic. 218 (1998), 256–268.Google Scholar
4Baricz, Á.. Landen-type inequality for Bessel functions. Computat. Meth. Funct. Theory 5 (2005), 373–379.Google Scholar
5Baricz, Á.. Functional inequalities involving special functions. J. Math. Analysis Applic. 319 (2006), 450–459.Google Scholar
6Baricz, Á.. Functional inequalities involving special functions. II. J. Math. Analysis Applic. 327 (2007), 1202–1213.Google Scholar
7Baricz, Á.. Functional inequalities for Galue's generalized modified Bessel functions. J. Math. Inequal. 1 (2007), 183–193.Google Scholar
8Baricz, Á.. Bounds for modified Bessel functions of the first and second kinds. Proc. Edinb. Math. Soc. 53 (2010), 575–599.Google Scholar
9Biernacki, M. and Krzyż, J.. On the monotonity of certain functionals in the theory of analytic functions. Annales Univ. Mariae Curie-Sklodowska A 9 (1955), 135–147.Google Scholar
10Heikkala, V., Vamanamurthy, M. K. and Vuorinen, M.. Generalized elliptic integrals. Computat. Meth. Funct. Theory 9 (2009), 75–109.Google Scholar
11Joshi, C. M. and Nalwaya, S.. Inequalities for modified Struve functions. J. Indian Math. Soc. 65 (1998), 49–57.Google Scholar
12Kalmykov, S. I. and Karp, D.. Log-concavity for series in reciprocal gamma functions and applications. Integ. Transf. Special Funct. 24 (2013), 859–872.Google Scholar
13Laforgia, A.. Bounds for modified Bessel functions. J. Computat. Appl. Math. 34 (1991), 263–267.Google Scholar
14Mitrinović, D. S.. Analytic inequalities (Springer, 1970).Google Scholar
15Olver, F. W. J., Lozier, D. W., Boisvert, R. F. and Clark, C. W. (eds). NIST handbook of mathematical functions (Cambridge University Press, 2010).Google Scholar
16Ponnusamy, S. and Vuorinen, M.. Asymptotic expansions and inequalities for hypergeometric functions. Mathematika 44 (1997), 43–64.Google Scholar