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

Abstract

Abstract 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 Chebychev’s inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the Hölder inequality, and introduce a Turán type mean inequality for the Kummer confluent k-hypergeometric function.

Keywords

• Extended gamma function
• Inequality
• Logarithmic convexity
• Confluent hypergeometric k-function