Wu, Shanhe; Srivastava, H. M. A further refinement of a Jordan type inequality and its application. (English) Zbl 1142.26019 Appl. Math. Comput. 197, No. 2, 914-923 (2008). Summary: By introducing Taylor polynomials, a new sharpened and generalized version of Jordan’s inequality is established. The result is then used to obtain a substantially more refined inequality of Jordan type. Moreover, an application of the results presented here toward the improvement of the Yang Le inequality is also considered in this paper. Cited in 1 ReviewCited in 18 Documents MSC: 26D15 Inequalities for sums, series and integrals Keywords:Jordan’s inequality; Taylor polynomials; higher order derivatives; Yang Le inequality; generalizations and sharpening of Jordan’s inequality PDF BibTeX XML Cite \textit{S. Wu} and \textit{H. M. Srivastava}, Appl. Math. Comput. 197, No. 2, 914--923 (2008; Zbl 1142.26019) Full Text: DOI OpenURL References: [1] Mitrinović, D.S.; Vasić, P.M., Analytic inequalities, (1970), Springer-Verlag Berlin, New York and Heidelberg · Zbl 0319.26010 [2] Wu, S.-H., On generalizations and refinements of Jordan type inequality, Octogon math. mag., 12, 267-272, (2004) [3] Wu, S.-H.; Debnath, L., A new generalized and sharp version of jordan’s inequality and its applications to the improvement of the Yang le inequality. II, Appl. math. lett., 20, 532-538, (2007) · Zbl 1162.26310 [4] S.-H. Wu, Sharpness and generalization of Jordan’s inequality and its application, Taiwanese J. Math. 12 (2) (2008). · Zbl 1180.26018 [5] Zhu, L., Sharpening jordan’s inequality and Yang le inequality, Appl. math. lett., 19, 240-243, (2006) · Zbl 1097.26012 [6] Zhu, L., Sharpening of jordan’s inequalities and its applications, Math. inequal. appl., 9, 103-106, (2006) · Zbl 1089.26007 [7] Zhu, L., Sharpening jordan’s inequality and Yang le inequality. II, Appl. math. lett., 19, 990-994, (2006) · Zbl 1122.26014 [8] Özban, A.Y., A new refined form of jordan’s inequality and its applications, Appl. math. lett., 19, 155-160, (2006) · Zbl 1109.26011 [9] Debnath, L.; Zhao, C.-J., New strengthened jordan’s inequality and its applications, Appl. math. lett., 16, 557-560, (2003) · Zbl 1041.26005 [10] C.-J. Zhao, L. Debnath, On generalizations of L. Yang’s inequality, J. Inequal. Pure Appl. Math. 3 (4) (2002) Article 56, pp. 1-5 (electronic). · Zbl 1023.26017 [11] Yuefeng, F., Jordan’s inequality, Math. mag., 69, 126-127, (1996) [12] Mercer, A.McD.; Abel, U.; Caccia, D., A sharpening of jordan’s inequality, Amer. math. monthly, 93, 568-569, (1986) [13] Wu, S.-H.; Srivastava, H.M., A weighted and exponential generalization of wilker’s inequality and its applications, Integral transform. spec. funct., 18, 529-535, (2007) · Zbl 1128.26017 [14] Wu, S.-H.; Srivastava, H.M., Some improvements and generalizations of steffensen’s integral inequality, Appl. math. comput., 192, 428-434, (2007) · Zbl 1193.26025 [15] Wu, S.-H.; Debnath, L., A new generalized and sharp version of jordan’s inequality and its applications to the improvement of the Yang le inequality, Appl. math. lett., 19, 1378-1384, (2006) · Zbl 1132.26334 [16] Anderson, G.D.; Vamanamurthy, M.K.; Vuorinen, M., Conformal invariants, inequalities, and quasiconformal maps (with 1 IBM-PC floppy disk), Canadian mathematical society series of monographs and advanced texts, (1997), A Wiley-Interscience Publication, John Wiley and Sons New York [17] Anderson, G.D.; Qiu, S.-L.; Vamanamurthy, M.K.; Vuorinen, M., Generalized elliptic integrals and modular equations, Pacific J. math., 192, 1-37, (2000) [18] Yang, L., Distribution of values and new research, (1982), Science Press Beijing, (in Chinese) 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.