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A weighted and exponential generalization of Wilker’s inequality and its applications. (English) Zbl 1128.26017

Summary: The authors first prove a weighted and exponential generalization of Wilker’s inequality. The main result presented here is then applied with a view to derive an improved version of the Sándor-Bencze inequality. Some other closely-related inequalities are also considered.

MSC:

26D15 Inequalities for sums, series and integrals
26D05 Inequalities for trigonometric functions and polynomials
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
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References:

[1] Wilker J. B., American Mathematical Monthly 96 (1989)
[2] DOI: 10.2307/2325035
[3] Guo B.-N., Inequality Theory and Applications 2 pp 109– (2003)
[4] Guo B.-N., RGMIA Research Report Collection 3 (2000)
[5] Guo B.-N., Mathematical Inequalities and Applications 6 pp 19– (2003) · Zbl 1040.26006
[6] Qi F., RGMIA Research Report Collection 9 (2006)
[7] DOI: 10.2307/4145099 · Zbl 1187.26010
[8] Zhu L., Mathematical Inequalities and Applications 8 pp 749– (2005) · Zbl 1084.26008
[9] Huygens C., Oeuvres Completes 1 (1888)
[10] Sándor J., RGMIA Research Report Collection 8 (2005)
[11] Hardy G. H., Inequalities, 2. ed. (1952)
[12] Mitrinović D. S., Analytic Inequalities (1970) · Zbl 0199.38101
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