Sub- and superadditive properties of Euler's gamma function

Abstract

Abstract. Let α > 0 and 0 < c = 1 be real numbers. The inequality Γ(x + y + c) Γ(x + y)

Quasilinearity of Some Composite Functionals With Applications

“…REMARK 5.7. For other examples of superadditive (subadditive) functionals that can provide interesting inequalities similar to the ones outlined above, we refer to [1,[6][7][8][9].…”

Inequalities involving the multiple psi function

“…Finding bounds for Euler's gamma function and multiple gamma functions and their ratios have been the subject of study of many mathematicians and researchers [1][2][3][4][5][6][8][9][10]12,15,18,19]. Subadditivity (superadditivity) is a part of the theory of…”

“…In [4], H. Alzer derived that (e x ) is strictly concave on R, where (x) = d dx log (x) is known as the psi (digamma) function. Recently, in 2007, H. Alzer [5] proved the subadditive and superadditive properties of Euler's gamma function, and obtained the following interesting inequality:…”

Accurate Estimates of the Gamma Function Involving the PSI Function

“…Recently, the problem of approximating of the gamma and polygamma functions and introducing new, accurate estimates has attracted the attention of many authors, see for example, [1,[3][4][5][6][7][8][9][10][11][12][13][14]22] and all references therein. In particular, we proved in [17] the following asymptotic formula, depending on real parameters b, c,…”