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Sharp Power Mean Bounds for Two Seiffert-like Means
Axioms, 2023 The mean is a subject of extensive study among scholars, and the pursuit of optimal power mean bounds is a highly active field. This article begins with a concise overview of recent advancements in this area, focusing specifically on Seiffert-like means.
Zhenhang Yang, Jing Zhang
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New Bounds for Arithmetic Mean by the Seiffert-like Means
Mathematics, 2022 By using the power series of the functions 1/sinnt and cost/sinnt (n=1,2,3,4,5), and the estimation of the ratio of two adjacent Bernoulli numbers, we obtained new bounds for arithmetic mean A by the weighted arithmetic means of Mtan1/3Msin2/3 and 13Mtan+
Ling Zhu
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Journal of Mathematical Inequalities, 2015 We investigate the representation of homogeneous, symmetric means in the form M(x,y)=\frac{x-y}{2f((x-y)/(x+y))}. This allows for a new approach to comparing means. As an example, we provide optimal estimate of the form (1- )min(x,y)+ max(x,y)<= M(x,y)<= (1- )min(x,y)+ max(x,y) and M((x+y)/2- (x-y)/2,(x+y)/2+ (x-y)/2)<= N(x,y)<= M ...
Witkowski, Alfred
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Refinements of bounds for the arithmetic mean by new Seiffert-like means
AIMS Mathematics, 2021 In the article, we present the sharp upper and lower bounds for the arithmetic mean in terms of new Seiffert-like means, which give some refinements of the results obtained in [1].
Wei-Mao Qian, Tie-Hong Zhao, Yu-Pei Lv
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Optimal bounds for Seiffert-like elliptic integral mean by harmonic, geometric, and arithmetic means
Journal of Inequalities and Applications, 2022 In this article, we present the optimal bounds for a special elliptic integral mean in terms of the harmonic combinations of harmonic, geometric, and arithmetic means.
Fan Zhang, Weimao Qian, Hui Zuo Xu
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Optimal bounds of the arithmetic mean in terms of new Seiffert-like means [PDF]
Mathematical Inequalities & Applications, 2020 In this paper, optimal bounds for the arithmetic means in terms of the arithmetic, harmonic, quadratic, inverse quadratic and geometric combination of means generated by sine, tangent, hyperbolic sine and hyperbolic tangent functions are derived and proved using the concept of Seiffert functions.
Nowicka, Monika, Witkowski, Alfred
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AIMS Mathematics, 2021 In this paper, optimal bounds for the sine and hyperbolic tangent means by arithmetic and centroidal means in exponential type are established using the monotone form of L'Hospital's rule and the criterion for the monotonicity of the quotient of power ...
Ling Zhu, Branko Malešević
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New Masjed Jamei–Type Inequalities for Inverse Trigonometric and Inverse Hyperbolic Functions
Mathematics, 2022 In this paper, we establish two new inequalities of the Masjed Jamei type for inverse trigonometric and inverse hyperbolic functions and apply them to obtain some refinement and extension of Mitrinović–Adamović and Lazarević inequalities.
Ling Zhu
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Optimal bounds for two Seiffert–like means in exponential type
Journal of Mathematical Analysis and Applications, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Optimal Bounds of the Arithmetic Mean by Harmonic, Contra-harmonic and New Seiffert-like Means
Asian Research Journal of Mathematics, 2020 We provide the optimal bounds for the arithmetic mean in terms of harmonic, contra-harmonic and new Seiffert-like means.
Wei-Mao Qian, Hui-Zuo Xu
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