AIMS Mathematics, 2019, 4(5): 1499-1507. doi: 10.3934/math.2019.5.1499

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Convexity and inequalities related to extended beta and confluent hypergeometric functions

1 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China
2 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
3 Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, China
4 Department of Mathematics, College of Arts and Science at Wadi Al Dawaser, Prince Sattam bin Abdulaziz University, Wadi Al Dawaser 11991, Kingdom of Saudi Arabia
5 Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal 18000, Upper Dir, Pakistan

In the paper, the authors establish the logarithmic convexity and some inequalities for the extended beta function and, by using these inequalities for the extended beta function, find the logarithmic convexity and the monotonicity for the extended confluent hypergeometric function.
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