GENERALIZED GUDERMANNIAN FUNCTION

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