About Trigonometric-Polynomial Bounds of Sinc Function

Dhaigude, Ramkrishna M.; Chesneau, Christophe; Bagul, Yogesh J.

doi:10.36753/mathenot.585735

Cited by 9 publications

(3 citation statements)

References 9 publications

(10 reference statements)

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“…Since the last two decades, there has been a growing interest in the field of inequalities involving trigonometric functions (see [4,6,7,10,13,15,16,18,21], and references therein). In this connection, R. Klén et al [13] proved the following inequalities:…”

Section: Introductionmentioning

confidence: 99%

Generalized bounds for sine and cosine functions

Bagul¹,

Chesnea

2021

Asian-European J. Math.

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Section: Introductionmentioning

confidence: 99%

Generalized bounds for sine and cosine functions

Bagul¹,

Chesnea

2021

Asian-European J. Math.

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“…In [22], L. Zhu obtained Cusa-Huygens type inequalities on a wider range (0, π). We must emphasize here that the sharp Cusa-Huygens type inequalities on a wider range (0, π) have also appeared in [5,10,15,17].…”

Section: Introductionmentioning

confidence: 81%

New Refinements of Cusa-Huygens inequality

Chesneau¹,

Kostić²,

Malešević³

et al. 2020

Preprint

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In the paper, we refine and extend Cusa-Huygens inequality by simple functions. In particular, we determine sharp bounds for sin(x)/x of the form (2 + cos(x))/3 − (2/3 − 2/π)Υ(x), where Υ(x) > 0 for x ∈ (0, π/2), Υ(0) = 0 and Υ(π/2) = 1, such that sin x/x and the proposed bounds coincide at x = 0 and x = π/2. The hierarchy of the obtained bounds is discussed, along with a graphical study. Also, alternative proofs of the main result are given.

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“…Furthermore, we can express these multivariate nonlinear trigonometric integral operators in simple forms for a broad range of univariate and multivariate functions f . With the aim of giving examples of applications, we combine some of the above properties to establish new trigonometric inequalities, which remain a contemporary topic (see [13], [3], [11] and [12], among others). To provide a direct visual check on them, figures are created.…”

Section: Motivationsmentioning

confidence: 99%

Novel Multivariate Integral Operators Incorporating Trigonometric Transformations

Chesneau

2024

Pan-Amer. J. Math.

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The creation of new nonlinear multivariate integral operators is motivated by the need for mathematical tools that can handle the complex interdependencies that naturally arise in contemporary applications. From an abstract scientific point of view, it is also necessary to develop new operator theories beyond existing ones to offer original research perspectives. This article contributes to these complementary aspects. We present two nonlinear multivariate integral operators that have the particularity of incorporating trigonometric transformations of the main function. Thanks to their trigonometric nature, they completely stand out from existing operators, offering a new and complete framework. Therefore, we take advantage of advanced mathematical techniques for trigonometric functions to address the challenges they pose. In particular, we show that they have manageable integrals and series expansions, that they are solutions of specific differential and functional equations, and that they are involved in general inequalities of various types (Hölder-type, convex-type, etc.). In the application part, we use some of these properties to propose a wide collection of trigonometric inequalities that are both original and precise. Figures are produced to illustrate them for a direct visual check.

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About Trigonometric-Polynomial Bounds of Sinc Function

Abstract: In this article, we establish sharp trigonometric-polynomial bounds for unnormalized sinc function.

Cited by 9 publications

References 9 publications

Generalized bounds for sine and cosine functions

Generalized bounds for sine and cosine functions

New Refinements of Cusa-Huygens inequality

Novel Multivariate Integral Operators Incorporating Trigonometric Transformations

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