TY - JOUR
T1 - APPLICATIONS OF A DUALITY BETWEEN GENERALIZED TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS II
AU - Miyakawa, Hiroki
AU - Takeuchi, Shingo
N1 - Funding Information:
The work of S. T. was supported by JSPS KAKENHI Grant Number 17K05336, 22K03392. ∗Corresponding author.
Publisher Copyright:
© 2022,Journal of Mathematical Inequalities.All Rights Reserved.
PY - 2022
Y1 - 2022
N2 - Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed) Cusa-Huygens-type inequalities for the generalized functions. In addition, multiple and double-angle formulas not previously obtained are also given.
AB - Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed) Cusa-Huygens-type inequalities for the generalized functions. In addition, multiple and double-angle formulas not previously obtained are also given.
KW - Cusa-huygens inequality
KW - Double-angle formula
KW - Generalized hyperbolic function
KW - Generalized trigonometric function
KW - Huygens inequality
KW - Mitrinovi ć-adamović inequality
KW - Multiple-angle formula
KW - P-laplacian.
KW - Wilker inequality
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U2 - 10.7153/jmi-2022-16-102
DO - 10.7153/jmi-2022-16-102
M3 - Article
AN - SCOPUS:85146702396
SN - 1846-579X
VL - 16
SP - 1571
EP - 1585
JO - Journal of Mathematical Inequalities
JF - Journal of Mathematical Inequalities
IS - 4
ER -