Abstract
This paper deals with thep-version of the Schwab-Borchardt mean. Lower and upper bounds for this mean, expressed in terms of the weighted geometric and arithmetic means of its variables, are obtained. Applications to four bivariate means, introduced earlier by the author of this paper, are included.
Highlights
In the past few years, there is a renewed interest in investigations of bivariate means
A remarkable result states that the mean SBp admits a representation in terms of the Gauss hypergeometric function
We close this section with definitions of some bivariate means used in the sequel
Summary
In the past few years, there is a renewed interest in investigations of bivariate means. The inverse functions sin−p1 and sinh−p1 are represented as follows [7]: sin−p1u tp)−1/p dt tp)−1/p dt International Journal of Mathematics and Mathematical Sciences We recall definition of a certain bivariate mean introduced recently in [1] We call SBp(x, y) the p-Schwab-Borchardt mean.
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