Dietrich Borchardt, the father

Interview mit Dietrich Dörner

Prof. Dr. sc. Dietrich Dörner studierte Psychologie an der Universität Kiel und wurde 1979 Professor für Allgemeine Psychologie an der Universität Bamberg. Von 1989 bis 1991 hatte er die Leitung der Arbeitsgruppe Kognitive Anthropologie am Berliner Max-Planck-Institut inne. Bis zu seiner Emeritierung im Sommer 2006 leitete er das Institut für Theoretische Psychologie an der Universität Bamberg....

1644 Dietrich Gotze and Ralph

On Some Means Derived from the Schwab–borchardt Mean Ii

Sharp bounds for four bivariate means derived from the Schwab-Borchardt mean are obtained. The bounding quantities are either geometric or arithmetic convex combinations of two generating means. The four means discussed in this paper have been introduced and studied in [13]. Mathematics subject classification (2010): 26E60, 26D05, 26D07.

Inequalities for the Schwab-Borchardt mean and their applications

Inequalities for the Schwab-Borchardt mean are obtained. They contain known results for the trigonometric and hyperbolic functions including those obtained by J. Wilker [15] and C. Huygens [5]. The main results of this paper can also be utilized to obtain new inequalities for some bivariate means including the logarithmic mean and two means introduced by Seiffert. Mathematics subject classifica...

On Some Means Derived from the Schwab–borchardt Mean

Bivariate means defined as the Schwab-Borchardt mean of two bivariate means are investigated. Explicit formulas for those means are obtained. It is demonstrated that they interpolate inequalities connecting the well known bivariate means. Optimal bounds for the means under discussion are also obtained. The bounding quantities are convex combinations of the generating means.