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Five Wilker Huygens-type inequalities involving Gudermannian and the inverse Gudermannian functions are obtained. The Schwab-Borchardt mean plays a crucial role in the proofs. Also, an analytical inequality for the sums of powers, established earlier by this author, is an indispensable tool in the the proofs of the main results of this paper.

WILKER AND HUYGENS-TYPE INEQUALITIES INVOLVING GUDERMANNIAN AND THE INVERSE GUDERMANNIAN FUNCTIONS