Erden, Samet Wirtinger type inequalities for higher order differentiable functions. (English) Zbl 1443.26012 Turk. J. Math. 44, No. 3, 656-661 (2020). Summary: In this work, we establish a Wirtinger type inequality which gives the relation between the integral of square of its any order derivative via Taylor’s formula. Then, we provide a similar inequality for mappings that are elements of \(L_r\) space with \(r > 1\). Also, we indicate that special cases of these inequalities give some results presented in the earlier works. Cited in 1 Document MSC: 26D15 Inequalities for sums, series and integrals 26D10 Inequalities involving derivatives and differential and integral operators 41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) Keywords:Wirtinger inequality; Taylor series PDFBibTeX XMLCite \textit{S. Erden}, Turk. J. Math. 44, No. 3, 656--661 (2020; Zbl 1443.26012) Full Text: DOI References: [1] Alzer H. A continuous and a discrete varaint of Wirtinger’s inequality. Mathematica Pannonica 1992; 3 (1): 83-89. · Zbl 0749.26011 [2] Alomari MW. On Beesack-Wirtinger Inequality. Results in Mathematics 2017; 72 (3):1213-1225. doi: 10.1007/s00025-016-0644-6 · Zbl 1376.26016 [3] Beesack PR. Hardy’s inequality and its extensions. Pacific Journal of Mathematics 1961; 11 (1): 39-61. · Zbl 0103.03503 [4] Beesack PR. Integral inequalities involving a function and its derivative. The American Mathematical Monthly 1971; 78 (7): 705-741. · Zbl 0223.26012 [5] Böttcher A, Widom H. From Toeplitz Eigenvalues through Green’s Kernels to Higher-order Wirtinger-Sobolev Inequalities. Advances and Applications 2006; 171: 73-87. · Zbl 1118.47016 [6] Diaz JB, Metcalf FT. Variations on Wirtinger’s inequality, in: Inequalities. USA: New York, Academic Press, 1967, pp. 79-103. [7] Gilbarg D, Trudinger N. Elliptic Partial Differential Equations of the Second Order. 2nd ed., Berlin, Springer, 1977. · Zbl 0361.35003 [8] Hardy GH, Littlewood JE, Pólya G. Inequalities. Cambridge University Press, 1988. [9] Li P, Treibergs A. Applications of Eigenvalue Techniques to Geometry. Contemporary Geometry: Zhong J-Q., Memorial Volume, Wu HH., ed., USA: New York, Plenum Press, 1991, pp. 22-95. [10] Osserman R. The isoperimetric inequality. Bulletin of the American Mathematical Society 1978; 84: 1182-1238. doi: 10.1090/S0002-9904-1978-14553-4 · Zbl 0411.52006 [11] Sarikaya MZ. On the new type Wirtinger inequality. Konuralp Journal of Mathematics 2019; 7 (1): 112-116. · Zbl 1438.26092 [12] Swanson CA. Wirtinger’s inequality. SIAM Journal on Mathematical Analysis 1978; 9 (3):484-491. doi: 10.1137/0509029 · Zbl 0402.26005 [13] Takahasi S-E, Miura T. 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.