Monotonicity and inequalities related to the generalized inverse Lemniscate functions

In the paper, we mainly studied the monotonicity and inequalities for some functions related to the generalized inverse lemniscate and the generalized hyperbolic inverse lemniscate functions. At first, we presented a bound estimation of the generalized inverse lemniscate functions by using Lerch Phi...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 116; no. 1
Main Authors: Yin, Li, Lin, Xiu Li
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.01.2022
Springer Nature B.V
Subjects:
Applications of Mathematics
Generalized inverse
Inequalities
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
Generalized trigonometric and hyperbolic functions
Generalized inverse lemniscate functions
33E05
26D07
Inequalities
33B10
ISSN:1578-7303, 1579-1505
Online Access:Get full text
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Summary:In the paper, we mainly studied the monotonicity and inequalities for some functions related to the generalized inverse lemniscate and the generalized hyperbolic inverse lemniscate functions. At first, we presented a bound estimation of the generalized inverse lemniscate functions by using Lerch Phi function. Finally, some Shafer-Fink, Wilker and Huygens type inequalities for the generalized inverse lemniscate and the generalized hyperbolic inverse lemniscate functions were obtained.
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ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-021-01194-1