Optimal bounds for the sine and hyperbolic tangent means II
-
Monika Nowicka
and
Alfred Witkowski
Abstract
We provide the optimal bounds for the sine and hyperbolic tangent means in terms of various weighted means of the arithmetic and the contraharmonic means.
References
[1] G. D. Anderson, M. K. Vamanamurthy and M. K. Vourinen, Conformal Invariants, Inequalities, and Quasiconformal Maps, Canad. Math. Soc. Ser. Monogr. Adv. Texts, John Wiley & Sons, New Yorks, 1997. Search in Google Scholar
[2] I. Lazarević, Certain inequalities with hyperbolic functions (in Serbo-Croatian), Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 159–170 (1966), 41–48. Search in Google Scholar
[3] M. Nowicka and A. Witkowski, Optimal bounds for the sine and hyperbolic tangent means, Punjab Univ. J. Math. (Lahore) 52 (2020), no. 5, 77–88. 10.1007/s00010-020-00705-6Search in Google Scholar
[4] A. Witkowski, On Seiffert-like means, J. Math. Inequal. 9 (2015), no. 4, 1071–1092. 10.7153/jmi-09-83Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
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- New generalized trapezoidal type integral inequalities with applications
- Existence of solutions of BVPs for fractional Langevin equations involving Caputo fractional derivatives
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Articles in the same Issue
- Frontmatter
- Localized optical vortex solitons in pair plasmas
- Exact solutions for the total variation denoising problem of piecewise constant images in dimension one
- New generalized trapezoidal type integral inequalities with applications
- Existence of solutions of BVPs for fractional Langevin equations involving Caputo fractional derivatives
- Some perturbed inequalities of Ostrowski type for high-order differentiable functions and applications
- Optimal bounds for the sine and hyperbolic tangent means II
- A piezoelectric contact problem with slip dependent friction and damage
- Extensions of coefficient estimates for new classes of bi-univalent functions defined by Sǎlǎgean integro-differential operator
- Blow-up of solutions for a Kirchhoff type equation with variable-exponent nonlinearities
- Caputo generalized ψ-fractional integral inequalities
- L1-solutions of the boundary value problem for implicit fractional order differential equations
- Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces
- On a family of the incomplete H-functions and associated integral transforms
- On strongly quasilinear elliptic systems with weak monotonicity
