Mondal Saiful R
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Hasa, Hofuf, 31982 Saudi Arabia.
J Inequal Appl. 2017;2017(1):10. doi: 10.1186/s13660-016-1276-9. Epub 2017 Jan 6.
We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions. The particular cases of those results also give the Turán-type inequalities for extended confluent and extended Gaussian hypergeometric functions. Some reverses of Turán-type inequalities are also derived.
我们研究了扩展贝塔函数的对数凸性。作为结果，我们建立了图兰型不等式。利用扩展贝塔函数的不等式推导出了扩展超几何函数的单调性、对数凸性和对数凹性。这些结果的特殊情况也给出了扩展合流超几何函数和扩展高斯超几何函数的图兰型不等式。还推导了一些图兰型不等式的反向不等式。
