Abstract
This paper deals with Huygens-type and Wilker-type inequalities for the generalized trigonometric functions of P. Lindqvist. A major mathematical tool used in this work is a generalized version of the Schwab-Borchardt mean introduced recently by the author of this work.
Highlights
The generalized trigonometric and the generalized hyperbolic functions have attracted attention of several researches
The goal of this paper is to establish some inequalities for families of functions mentioned earlier
A remarkable result states that the mean SBp admits a representation in terms of the Gauss hypergeometric function
Summary
The generalized trigonometric and the generalized hyperbolic functions have attracted attention of several researches. These functions, introduced by Lindqvist in [1], depend on one parameter p > 1. They become classical trigonometric and hyperbolic functions when p = 2. The goal of this paper is to establish some inequalities for families of functions mentioned earlier .
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