Abstract:
Wilker and Huygens-type inequalities involving generalized Gudermannian function and its inverse function are established. These results are obtained with the aid of the $p$-version of the Schwab–Borchardt mean. Generalized one-parameter trigonometric and hyperbolic functions play a crucial role in this paper.
Keywords:Generalized Gudermannian function and its inverse function; generalized trigonometric and generalized hyperbolic functions; Gauss hypergeometric function; $p$-version of the Schwab–Borchardt mean; inequalities.
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