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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Vydané v:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Ročník 116; číslo 1
Hlavní autori: Yin, Li, Lin, Xiu Li
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.01.2022
Springer Nature B.V
Predmet:
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
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Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-021-01194-1