×

Double-sided Taylor’s approximations and their applications in theory of trigonometric inequalities. (English) Zbl 1442.30002

Raigorodskii, Andrei M. (ed.) et al., Trigonometric sums and their applications. Cham: Springer. 159-167 (2020).
Summary: In this paper the double-sided Taylor’s approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
For the entire collection see [Zbl 1443.39001].

MSC:

30A10 Inequalities in the complex plane

References:

[1] D.S. Mitrinović, Analytic Inequalities (Springer, Berlin, 1970) · Zbl 0199.38101 · doi:10.1007/978-3-642-99970-3
[2] G. Milovanović, M. Rassias (eds.), Topics in special functions III, in Analytic Number Theory, Approximation Theory and Special Functions, ed. by G.D. Anderson, M. Vuorinen, X. Zhang (Springer, New York, 2014), pp. 297-345 · Zbl 1286.00055 · doi:10.1007/978-1-4939-0258-3
[3] M.J. Cloud, B.C. Drachman, L.P. Lebedev, Inequalities with Applications to Engineering (Springer, Cham, 2014) · Zbl 1295.26002
[4] C. Mortici, The natural approach of Wilker-Cusa-Huygens inequalities. Math. Inequal. Appl. 14(3), 535-541 (2011) · Zbl 1222.26020
[5] B. Malešević, M. Makragić, A method for proving some inequalities on mixed trigonometric polynomial functions. J. Math. Inequal. 10(3), 849-876 (2016) · Zbl 1351.26030 · doi:10.7153/jmi-10-69
[6] M. Makragić, A method for proving some inequalities on mixed hyperbolic-trigonometric polynomial functions. J. Math. Inequal. 11(3), 817-829 (2017) · Zbl 1373.26017 · doi:10.7153/jmi-2017-11-63
[7] T. Lutovac, B. Malešević, C. Mortici, The natural algorithmic approach of mixed trigonometric-polynomial problems. J. Inequal. Appl. 2017(116), 1-16 (2017) · Zbl 1373.42003
[8] B. Malešević, M. Rašajski, T. Lutovac, Refinements and generalizations of some inequalities of Shafer-Fink’s type for the inverse sine function. J. Inequal. Appl. 2017(275), 1-9 (2017) · Zbl 1374.26034
[9] H. Alzer, M.K. Kwong, On Jordan’s inequality. Period. Math. Hung. 77(2), 191-200 (2018) · Zbl 1413.26031 · doi:10.1007/s10998-017-0230-z
[10] B. Malešević, T. Lutovac, M. Rašajski, C. Mortici, Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities. Adv. Differ. Equ. 2018(90), 1-15 (2018) · Zbl 1445.26015
[11] M. Rašajski, T. Lutovac, B. Malešević, Sharpening and generalizations of Shafer-Fink and Wilker type inequalities: a new approach. J. Nonlinear Sci. Appl. 11(7), 885-893 (2018) · Zbl 1438.33002 · doi:10.22436/jnsa.011.07.02
[12] M. Rašajski, T. Lutovac, B. Malešević, About some exponential inequalities related to the sinc function. J. Inequal. Appl. 2018(150), 1-10 (2018) · Zbl 1427.26004
[13] T. Lutovac, B. Malešević, M. Rašajski, A new method for proving some inequalities related to several special functions. Results Math. 73(100), 1-15 (2018) · Zbl 1400.33001
[14] M. Nenezić, L. Zhu, Some improvements of Jordan-Steckin and Becker-Stark inequalities. Appl. Anal. Discrete Math. 12, 244-256 (2018) · Zbl 1499.41020 · doi:10.2298/AADM1801244N
[15] B. Malešević, M. Rasajski, T. Lutovac, Double-sided Taylor’s approximations and their applications in theory of analytic inequalities, in Differential and Integral Inequalities, ed. by D. Andrica, T. Rassias. Springer Optimization and Its Applications, vol. 151 (Springer, 2019), pp. 569-582. https://doi.org/10.1007/978-3-030-27407-8_20 · Zbl 1441.41009 · doi:10.1007/978-3-030-27407-8_20
[16] J. Sándor, On D’aurizio’s trigonometric inequality. J. Math. Inequal. 10(3), 885-888 (2016) · Zbl 1349.26035 · doi:10.7153/jmi-10-71
[17] J. D’Aurizio, Refinements of the Shafer-Fink inequality of arbitrary uniform precision. Math. Inequal. Appl. 17(4), 1487-1498 (2014) · Zbl 1304.26014
[18] B.D. Banjac, System for automatic proving of some classes of analytic inequalities. Doctoral dissertation (in Serbian), School of Electrical Engineering, Belgrade, May 2019. Available on: http://nardus.mpn.gov.rs/
[19] S.-H. Wu, L. Debnath, A generalization of L’Hospital-type rules for monotonicity and its application. Appl. Math. Lett. 22(2), 284-290 (2009) · Zbl 1163.26312 · doi:10.1016/j.aml.2008.06.001
[20] S.-H. Wu, H.M. Srivastva, A further refinement of a Jordan type inequality and its applications. Appl. Math. Comput. 197, 914-923 (2008) · Zbl 1142.26019
[21] S.-H. Wu, L. Debnath, Jordan-type inequalities for differentiable functions and their applications. Appl. Math. Lett. 21(8), 803-809 (2008) · Zbl 1168.26319 · doi:10.1016/j.aml.2007.09.001
[22] S.-H. Wu, H.M. Srivastava, A further refinement of Wilker’s inequality. Integral Transforms Spec. Funct. 19(9-10), 757-765 (2008) · Zbl 1176.11008 · doi:10.1080/10652460802340931
[23] I.S. Gradshteyn, I.M Ryzhik, Table of Integrals Series and Products, 8th edn. (Academic Press, San Diego, 2015) · Zbl 0918.65002
[24] B. Banjac, M. Nenezić, B. Malešević, Some applications of Lambda-method for obtaining approximations in filter design, in Proceedings of 23-rd TELFOR Conference, Beograd, 2015, pp. 404-406
[25] M. Nenezić, B. Malešević, C. Mortici, New approximations of some expressions involving trigonometric functions. Appl. Math. Comput. 283, 299-315 (2016) · Zbl 1410.26025
[26] B. Banjac, M. Makragić, B. Malešević, Some notes on a method for proving inequalities by computer. Results Math. 69(1), 161-176 (2016) · Zbl 1332.41008 · doi:10.1007/s00025-015-0485-8
[27] B. Malešević, I. Jovović, B. Banjac, A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions. J. Math. Inequal. 11(1), 151-162 (2017) · Zbl 1357.26024 · doi:10.7153/jmi-11-15
[28] B. Malešević, T. Lutovac, B. Banjac, A proof of an open problem of Yusuke Nishizawa for a power-exponential function. J. Math. Inequal. 12(2), 473-485 (2018) · Zbl 1395.26001 · doi:10.7153/jmi-2018-12-35
[29] B. Malešević, M. Rašajski, T. Lutovac, Refined estimates and generalizations of inequalities related to the arctangent function and Shafer’s inequality. Math. Probl. Eng. 2018, Article ID 4178629, 1-8 · Zbl 1427.26004
[30] B. · Zbl 1499.26060 · doi:10.2298/FIL1820921M
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.