Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities

被引:38
作者
Malesevic, Branko [1 ]
Lutovac, Tatjana [1 ]
Rasajski, Marija [1 ]
Mortici, Cristinel [2 ,3 ,4 ]
机构
[1] Univ Belgrade, Sch Elect Engn, Belgrade, Serbia
[2] Valahia Univ Targoviste, Targoviste, Romania
[3] Acad Romanian Scientists, Bucharest, Romania
[4] Univ Politehn Bucuresti, Bucharest, Romania
关键词
Sharpening; Generalization; Wilker-Cusa-Huygens's inequalities; Sine and cosine functions; Leibniz's theorem for alternating series;
D O I
10.1186/s13662-018-1545-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens type.
引用
收藏
页数:15
相关论文
共 16 条
[1]  
Agarwal RP., 1992, DIFFERENCE EQUATIONS
[2]  
Anderson G. D., 2014, Analytic number theory, approximation theory, and special functions, P297, DOI [10.1007/978-1-4939-0258-3_11, DOI 10.1007/978-1-4939-0258-3_11]
[3]  
[Anonymous], 1970, Analytic Inequalities
[4]   THE NATURAL APPROACH OF TRIGONOMETRIC INEQUALITIES - PADE APPROXIMANT [J].
Bercu, Gabriel .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2017, 11 (01) :181-191
[6]  
Gradshteyn I. S., 2015, Table of integrals, series, and products
[7]   The natural algorithmic approach of mixed trigonometric-polynomial problems [J].
Lutovac, Tatjana ;
Malesevic, Branko ;
Mortici, Cristinel .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
[8]   A METHOD FOR PROVING SOME INEQUALITIES ON MIXED HYPERBOLIC-TRIGONOMETRIC POLYNOMIAL FUNCTIONS [J].
Makragic, Milica .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2017, 11 (03) :817-829
[9]  
Malesevic B., ARXIV171103786
[10]  
Malesevic B., ARXIV171203772