On Jordan’s inequality

Alzer, Horst; Kwong, Man Kam

doi:10.1007/s10998-017-0230-z

Cited by 10 publications

(5 citation statements)

References 7 publications

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“…Let us mention that in papers [8], [18], [22], [25], [26] and [27] double-sided TAYLOR's approximations are used to obtain corresponding inequalities. Results of these papers can be further organized and made more precise using Theorem 4 so we get the order among the functions occurring within these inequalities.…”

Section: Discussionmentioning

confidence: 99%

Double–Sided Taylor’s Approximations and Their Applications in Theory of Analytic Inequalities

Malešević

Lutovac

Rašajski

et al. 2019

Differential and Integral Inequalities

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In this paper the double-sided TAYLOR's approximations are studied. A short proof of a well-known theorem on the double-sided TAYLOR's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such approximations. Then we present some new applications of the double-sided TAYLOR's approximations in the theory of analytic inequalities.Similarly, the first TAYLOR's approximation in the left neighborhood of b is defined by:

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Section: Discussionmentioning

confidence: 99%

Double–Sided Taylor’s Approximations and Their Applications in Theory of Analytic Inequalities

Malešević

Lutovac

Rašajski

et al. 2019

Differential and Integral Inequalities

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“…Since then, many authors have worked on extensions and improvements of Jordan's inequality [1][2][3][4][5][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] . In [8], F. Qi, D.-W. Niu and B.-N. Guo did the elaborate research, summarizing previously discovered improvements and applications of Jordan's inequality, along with related problems.…”

Section: Introductionmentioning

confidence: 99%

Jordan-Type Inequalities and Stratification

Mićović,

Malešević

2024

Preprint

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In this paper, two double Jordan-type inequalities are introduced based on the papers [1]-[5]. These inequalities generalize the inequalities obtained in [1]-[5]. As a result, some new upper and lower bounds of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions elaborated in [6]. Based on this approach, some optimal approximations of the sinc function are derived by determining corresponding minimax approximants, also described in the paper [6].

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“…Particularly, their application in proving various analytic inequalities is of great importance [6], [12], [16], [17]. Recently, numerous inequalities have been generalized and improved by the use of the so-called doublesided TAYLOR's approximations [16], [20], [21]- [25] and [29]. Many topics regarding these approximations are presented in [29].…”

Section: Introductionmentioning

confidence: 99%