Convexity, Schur-convexity and bounds for the gamma function involving the digamma function (Q1293513)

With aid of, among others, Jensen-convex and Schur-convex functions the author offers considerable improvements on estimations of a shifted gamma function divided by the gamma function at the original place. In particular, considerable improvements on chains of inequalities in the paper of \textit{H. Alzer} [Math. Comput. 60, No. 201, 337-346 (1993; Zbl 0802.33001)] are offered. The paper concludes with remarks on \textit{J. Gurland}'s [Skand. Aktuarietidskr. 39, 171-172 (1957; Zbl 0089.28201)] results on iteration of the previous shift-and-divide process.