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