Abstract
In this paper, we prove that for x + y > 0 and y + 1 > 0 the inequality [ Γ ( x + y + 1 ) / Γ ( y + 1 ) ] 1 / x [ Γ ( x + y + 2 ) / Γ ( y + 1 ) ] 1 / ( x + 1 ) < ( x + y x + y + 1 ) 1 / 2 is valid if x > 1 and reversed if x < 1 and that the power 1 2 is the best possible, where Γ ( x ) is the Euler gamma function. This extends the result of [Y. Yu, An inequality for ratios of gamma functions, J. Math. Anal. Appl. 352 (2) (2009) 967–970] and resolves an open problem posed in [B.-N. Guo, F. Qi, Inequalities and monotonicity for the ratio of gamma functions, Taiwanese J. Math. 7 (2) (2003) 239–247].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
