TY - JOUR
AU - Baricz, Árpád
AU - Ponnusamy, Saminathan
AU - Vuorinen, Matti
TI - Functional inequalities for modified Bessel functions
JF - EXPOSITIONES MATHEMATICAE
J2 - EXPO MATH
VL - 29
PY - 2011
IS - 4
SP - 399
EP - 414
PG - 16
SN - 0723-0869
DO - 10.1016/j.exmath.2011.07.001
UR - https://m2.mtmt.hu/api/publication/1775537
ID - 1775537
AB - 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.
LA - English
DB - MTMT
ER -
TY - JOUR
AU - András, Szilárd
AU - Baricz, Árpád
TI - Bounds for complete elliptic integrals of the first kind
JF - EXPOSITIONES MATHEMATICAE
J2 - EXPO MATH
VL - 28
PY - 2010
IS - 4
SP - 357
EP - 364
PG - 8
SN - 0723-0869
DO - 10.1016/j.exmath.2009.12.005
UR - https://m2.mtmt.hu/api/publication/1385763
ID - 1385763
AB - 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.
LA - English
DB - MTMT
ER -
TY - BOOK
AU - Baricz, Árpád
TI - Generalized Bessel functions of the first kind
T3 - Lecture Notes in Mathematics, ISSN 0075-8434
ET - 0
PB - Springer-Verlag
CY - Berlin
CY - Heidelberg
PY - 2010
SP - 200
SN - 9783642122293
DO - 10.1007/978-3-642-12230-9
UR - https://m2.mtmt.hu/api/publication/1353029
ID - 1353029
AB - 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.
LA - English
DB - MTMT
ER -
TY - JOUR
AU - Baricz, Árpád
TI - Geometrically concave univariate distributions
JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
J2 - J MATH ANAL APPL
VL - 363
PY - 2010
IS - 1
SP - 182
EP - 196
PG - 15
SN - 0022-247X
DO - 10.1016/j.jmaa.2009.08.029
UR - https://m2.mtmt.hu/api/publication/1352972
ID - 1352972
AB - 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.
LA - English
DB - MTMT
ER -
TY - JOUR
AU - Baricz, Árpád
TI - Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means
JF - JOURNAL OF INEQUALITIES IN PURE AND APPLIED MATHEMATICS
J2 - J INEQUAL PURE APPL MATH
VL - 8
PY - 2007
IS - 2
SP - 1
EP - 9
PG - 9
SN - 1443-5756
UR - https://m2.mtmt.hu/api/publication/1416258
ID - 1416258
AB - In this note we investigate the convexity of zero-balanced Gaussian hypergeometric functions and general power series with respect to Hölder means.
LA - English
DB - MTMT
ER -
TY - JOUR
AU - Baricz, Árpád
TI - Turán type inequalities for generalized complete elliptic integrals
JF - MATHEMATISCHE ZEITSCHRIFT
J2 - MATH Z
VL - 256
PY - 2007
IS - 4
SP - 895
EP - 911
PG - 17
SN - 0025-5874
DO - 10.1007/s00209-007-0111-x
UR - https://m2.mtmt.hu/api/publication/1353025
ID - 1353025
AB - 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.
LA - English
DB - MTMT
ER -