@article{MTMT:1775537,
author = {Baricz, Árpád and Ponnusamy, Saminathan and Vuorinen, Matti},
doi = {10.1016/j.exmath.2011.07.001},
title = {Functional inequalities for modified Bessel functions},
journal-iso = {EXPO MATH},
journal = {EXPOSITIONES MATHEMATICAE},
volume = {29},
unique-id = {1775537},
issn = {0723-0869},
abstract = {In this paper, our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kind. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Turán-type inequalities for these functions. As an application of the results concerning the modified Bessel function of the second kind, we prove that the cumulative distribution function of the gamma–gamma distribution is log-concave. At the end of this paper, several open problems are posed, which may be of interest for further research.},
year = {2011},
pages = {399-414}
}
@article{MTMT:1385763,
author = {András, Szilárd and Baricz, Árpád},
doi = {10.1016/j.exmath.2009.12.005},
title = {Bounds for complete elliptic integrals of the first kind},
journal-iso = {EXPO MATH},
journal = {EXPOSITIONES MATHEMATICAE},
volume = {28},
unique-id = {1385763},
issn = {0723-0869},
abstract = {In this note by using some elementary computations we present some new sharp lower and upper bounds for the complete elliptic integrals of the first kind. These results improve some known bounds in the literature and are deduced from the well-known Wallis inequality, which has been studied extensively in the last 10 years.},
year = {2010},
pages = {357-364}
}
@book{MTMT:1353029,
isbn = {9783642122293},
author = {Baricz, Árpád},
doi = {10.1007/978-3-642-12230-9},
title = {Generalized Bessel functions of the first kind},
publisher = {Springer-Verlag, Berlin, Heidelberg},
unique-id = {1353029},
abstract = {In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions.},
year = {2010}
}
@article{MTMT:1352972,
author = {Baricz, Árpád},
doi = {10.1016/j.jmaa.2009.08.029},
title = {Geometrically concave univariate distributions},
journal-iso = {J MATH ANAL APPL},
journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
volume = {363},
unique-id = {1352972},
issn = {0022-247X},
abstract = {In this paper our aim is to show that if a probability density function is geometrically concave (convex), then the corresponding cumulative distribution function and the survival function are geometrically concave (convex) too, under some assumptions. The proofs are based on the so-called monotone form of l'Hospital's rule and permit us to extend our results to the case of the concavity (convexity) with respect to Hölder means. To illustrate the applications of the main results, we discuss in details the geometrical concavity of the probability density function, cumulative distribution function and survival function of some common continuous univariate distributions. Moreover, at the end of the paper, we present a simple alternative proof to Schweizer's problem related to the Mulholland's generalization of Minkowski's inequality.},
year = {2010},
eissn = {1096-0813},
pages = {182-196}
}
@article{MTMT:1416258,
author = {Baricz, Árpád},
title = {Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means},
journal-iso = {J INEQUAL PURE APPL MATH},
journal = {JOURNAL OF INEQUALITIES IN PURE AND APPLIED MATHEMATICS},
volume = {8},
unique-id = {1416258},
issn = {1443-5756},
abstract = {In this note we investigate the convexity of zero-balanced Gaussian hypergeometric functions and general power series with respect to Hölder means.},
year = {2007},
pages = {1-9}
}
@article{MTMT:1353025,
author = {Baricz, Árpád},
doi = {10.1007/s00209-007-0111-x},
title = {Turán type inequalities for generalized complete elliptic integrals},
journal-iso = {MATH Z},
journal = {MATHEMATISCHE ZEITSCHRIFT},
volume = {256},
unique-id = {1353025},
issn = {0025-5874},
abstract = {In this paper our aim is to establish some Turán type inequalities for Gaussian hypergeometric functions and for generalized complete elliptic integrals. These results complete the earlier result of P. Turán proved for Legendre polynomials. Moreover we show that there is a close connection between a Turán type inequality and a sharp lower bound for the generalized complete elliptic integral of the first kind. At the end of this paper we prove a recent conjecture of T. Sugawa and M. Vuorinen related to estimates of the hyperbolic distance of the twice punctured plane.},
year = {2007},
eissn = {1432-8232},
pages = {895-911}
}