Results 81 to 90 of about 18,466 (195)
Inequalities On Generalized Trigonometric Functions [PDF]
Proceedings of the 2016 3rd International Conference on Mechatronics and Information Technology, 2016 when 2, p = the p − functions sin p , cos p , tan p become our familiar trigonometric functions. Recently, the generalized trigonometric functions have been studied by many mathematicians from different viewpoints(see [2,4,5,6,7]). In [5,9], the authors gave basic properties of the generalized trigonometric functions.
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Some Identities and inequalities related to the Riemann zeta function
Moroccan Journal of Pure and Applied Analysis, 2019 A new proof of Euler’s formular for calculating ζ(2k) is given. Some new inequalities and identities for ζ(2k + 1) have also been given. The Riemann’s functional equation together with trigonometric identities were used to establish the results.
Abe-I-Kpeng Gregory +2 more
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On a Trigonometric Inequality of Vinogradov
Journal of Number Theory, 1994 Let \(m>1\) and \(n>0\) be integers. The author considers the sum \[ f(m,n)= \sum_{k=1}^{m-1} (|\sin (\pi kn/m)|) (\sin (\pi k/m))^{- 1}, \] which occurs in bounding incomplete exponential sums. He shows that \[ f(m,n)< \textstyle {{{4m} \over {\pi^ 2}} \bigl(\log m+ \gamma+ {1\over 8}-\log {\pi\over 2} \bigr) +{2\over \pi} \bigl( 2- {1\over \pi} \bigr)
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On the p-Version of the Schwab-Borchardt Mean
International Journal of Mathematics and Mathematical Sciences, 2014 This paper deals with a one-parameter generalization of the Schwab-Borchardt mean. The new mean is defined in terms of the inverse functions of the generalized trigonometric and generalized hyperbolic functions.
Edward Neuman
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On a trigonometric inequality of vinogradov
Journal of Number Theory, 1987 For positive integers \(m, n\) with \(m>1\) let \[ f(m,n)=\sum_{a=1}^{m-1}| \sin (\pi an/m)| / | \sin (\pi a/m)|. \] This sum arises in bounding incomplete exponential sums. \textit{I. M. Vinogradov} [Elements of number theory. New York: Dover (1954; Zbl 0057.28201)] showed that \(f(m,n)
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On Applicability of the Relaxation Spectrum of Fractional Maxwell Model to Description of Unimodal Relaxation Spectra of Polymers. [PDF]
Polymers (Basel), 2023 Stankiewicz A.
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Convex functions and inequalities in the secondary school
Lietuvos Matematikos Rinkinys, 2008 A function f : Df → R is called convex if for any x, y ∈ Df the inequality f ( x+y/2 ) \leq (f (x)+f (y) )/2 holds. We prove the main property of the convex fonctions (inequality (4)) and also the inequalities which the arithmetic, geometric, harmonic ...
Juozas Šinkūnas
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Solutions of two open problems on inequalities involving trigonometric and hyperbolic functions
CuboIn 2019, Bagul et al. posed two open problems dealing with inequalities involving trigonometric and hyperbolic functions and an adjustable parameter. This article is an attempt to solve these open problems.
Rupali Shinde +2 more
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A separation of some Seiffert-type means by power means
Journal of Numerical Analysis and Approximation Theory, 2012 Consider the identric mean \(\mathcal{I}\), the logarithmic mean \(\mathcal{L,}\) two trigonometric means defined by H. J. Seiffert and denoted by \(\mathcal{P}\) and \(\mathcal{T,}\) and the hyperbolic mean \(\mathcal{M}\) defined by E.
Iulia Costin, Gheorghe Toader
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