On the Schwab-Borchardt mean. II. (English) Zbl 1100.26011

Neuman, Edward; Sándor, József

Math. Pannonica 17, No. 1, 49-59 (2006).

Summary: This paper deals with the inequalities involving the Schwab-Borchardt mean and other bivariate means including those introduced by H.-J. Seiffert in [Problem 887, Nieuw Arch. Wisk 11, p. 176 (1993) and Aufgabe 16, Wurzel 29, p. 87 (1995)]. The main results of this paper are obtained using a representation of the Schwab-Borchardt mean in terms of the \(R\)-hypergeometric functions of two variables. The Ky Fan type inequalities for the particular means contained in the family of the Schwab-Borchardt means are also included. See also Part I by the same authors [Math. Pannonica 14, No. 2, 253–266 (2003; Zbl 1053.26015)].

MSC:

26D15	Inequalities for sums, series and integrals
26E60	Means

Keywords:

inequalities; Seiffert means; \(R\)-hypergeometric functions; Ky Fan type inequalities