Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function

Kottakkaran Sooppy Nisar, Feng Qi, Gauhar Rahman, Shahid Mubeen, and Muhammad Arshad, Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric $k$-function, Journal of Inequalities and Applications 2018, Paper No. 135, 12 pages; available online at https://doi.org/10.1186/s13660-018-1717-8.; International audience; In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric $k$-function via some classical inequalities such as the Chebychev inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the H\"older inequality, and introduce a Tur\'an type mean inequality for the Kummer confluent $k$-hypergeometric function.