Certain inequalities involving fractional powers

Abstract

The note re-examines Brown's new inequalities involving polynomials and fractional powers. Shorter proofs are provided, and greater attention is given to the conditions for the inequalities to hold.

On two lemmas of Brown and Shepp having application to sum sets and fractals, III

“…Establishing the canonical univariate inequalities can be quite tricky and some effort has been put into sharpening techniques for their derivation (see [7,11,[14][15][16][17] and most recently [1]). The 'two lemmas' of the title are special cases of the two parts of Theorem 3.2 below, the earliest versions of which are due to Brown and Shepp [7] and have influenced further work in the area.…”

Comments on some inequalities of Pearce and Pečarić

“…These inequalities were reexamined by A. W. Kemp [4] in 1992. In order to shorten the proof of Brown's main theorem, Kemp applied a specific inequality for convex functions which was generalized by C. E. M. Pearce and J. E. Pecaric.…”

“…The study of singular measures led G. Brown [1] in 1988 to several interesting new inequalities involving polynomials and fractional powers. These inequalities were reexamined by A. W. Kemp [4] in 1992. In order to shorten the proof of Brown's main theorem, Kemp applied a specific inequality for convex functions which was generalized by C. E. M. Pearce and J. E. Pecaric.…”