@article{MTMT:1385763, title = {Bounds for complete elliptic integrals of the first kind}, url = {https://m2.mtmt.hu/api/publication/1385763}, author = {András, Szilárd and Baricz, Árpád}, doi = {10.1016/j.exmath.2009.12.005}, 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}, eissn = {1878-0792}, pages = {357-364} } @article{MTMT:1416258, title = {Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means}, url = {https://m2.mtmt.hu/api/publication/1416258}, author = {Baricz, Árpád}, 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, title = {Turán type inequalities for generalized complete elliptic integrals}, url = {https://m2.mtmt.hu/api/publication/1353025}, author = {Baricz, Árpád}, doi = {10.1007/s00209-007-0111-x}, 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} }