Results 21 to 30 of about 18,585 (194)
Journal of Inequalities and Applications, 2016 An interplay between the sum of certain series related to harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits us to find ...
Omran Kouba
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Fractal and Fractional, 2023 This article extends the study of q-versions of analytic functions by introducing and studying the association of starlike functions with trigonometric cosine functions, both defined in their q-versions.
Yusra Taj +5 more
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On some inequalities for the identric, logarithmic and related means [PDF]
, 2015 We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.Comment:
Bhayo, Barkat Ali, Sándor, József
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New Refinements and Improvements of Some Trigonometric Inequalities Based on Padé Approximant
Journal of Mathematics, 2020 A multiple-point Padé approximant method is presented for approximating and bounding some trigonometric functions in this paper. We give new refinements and improvements of some trigonometric inequalities including Jordan’s inequality, Kober’s inequality,
Lina Zhang, Xuesi Ma
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Nikol’skii–Type Inequalities for Trigonometric Polynomials for Lorentz–Zygmund Spaces
Journal of Function Spaces, 2020 Nikol’skii–type inequalities, that is inequalities between different metrics of trigonometric polynomials on the torus Td for the Lorentz–Zygmund spaces, are obtained. The results of previous paper “Nikol’skii inequalities for Lorentz–Zygmund spaces” are
Leo R. Ya. Doktorski
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Padé approximant related to remarkable inequalities involving trigonometric functions
Journal of Inequalities and Applications, 2016 In this paper we, respectively, give simple proofs of some remarkable trigonometric inequalities, based on the Padé approximation method. We also obtain rational refinements of these inequalities.
Gabriel Bercu
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A Gronwall-type Trigonometric Inequality [PDF]
The American Mathematical Monthly, 2018 We prove that the absolute value of the $n$th derivative of $\cos(\sqrt{x})$ does not exceed $n!/(2n)!$ for all $x>0$ and $n = 0,1,\ldots$ and obtain a natural generalization of this inequality involving the analytic continuation of $\cos(\sqrt{x})$.
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On Huygens' Inequalities and the Theory of Means
International Journal of Mathematics and Mathematical Sciences, 2012 By using the theory of means, various refinements of Huygens' trigonometric and hyperbolic inequalities will be proved. New Huygens' type inequalities will be provided, too.
József Sándor
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Padé approximants for inverse trigonometric functions and their applications
Journal of Inequalities and Applications, 2017 The Padé approximation is a useful method for creating new inequalities and improving certain inequalities. In this paper we use the Padé approximant to give the refinements of some remarkable inequalities involving inverse trigonometric functions, it is
Shanhe Wu, Gabriel Bercu
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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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