In the article, presented are sufficient and necessary conditions for a class of functions involving the ratio of two gamma functions to be logarithmically completely monotonic. From this, some inequalities for bounding the ratio of two gamma functions are refined, extended and sharpened readily, and double inequalities on the divided differences of the psi and polygamma functions are derived s...

A novel definition of the divided difference is shown to lead most readily to the standard basic properties of the divided difference.

In the present paper, necessary and sufficient conditions are established for a function involving divided differences of the digamma and trigamma functions to be completely monotonic. Consequently, necessary and sufficient conditions are derived for a function involving the ratio of two gamma functions to be logarithmically completely monotonic, and some double inequalities are deduced for bou...

We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with posit...

Abstract. In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio of two ...

Received (Day Month Year) Revised (Day Month Year) Communicated by (xxxxxxxxxx) Fractional B-splines are a natural extension of classical B-splines. In this short paper, we show their relations to fractional divided differences and fractional difference operators , and present a generalized Hermite-Genochi formula. This formula then allows the definition of a larger class of fractional B-splines.

1 Divided Power Algebra—October 31, 2016 1 1.1 Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Extension of Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Compatible Divided Power structure . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Divided Power Algebra Associated to a Module . . . . . . . . . . . . . . . . . 5 1.5...

This paper is devoted to an inequality for divided differences in the multivariate case which is similar to the inequality obtained by [J. Pečarić, and M. Rodić Lipanović, On an inequality for divided differences, Asian-European Journal of Mathematics, Vol. 1, No. 1 (2008), 113-120].