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 -