On the New Wirtinger Type Inequalities

Year 2019, Volume: 7 Issue: 1, 112 - 116, 15.04.2019

Mehmet Zeki Sarıkaya

https://izlik.org/JA66UK37FR

Abstract

The aim of this paper to establish a generalized and refinement of Wirtinger type inequality.

Keywords

Wirtinger inequality , Hölder's inequality.

References

• [1] R. P. Agarwal and P. Y. H. Pang, Remarks on the generalizations of Opial’s inequality, J. Math. Anal. Appl. 190:2 (1995), 559–577.
• [2] M. W. Alomari, On Beesack–Wirtinger Inequality, Results Math 72 (2017), 1213–1225
• [3] P. R. Beesack, Integral inequalities involving a function and its derivative, Amer. Math. Monthly 78 (1971), 705–741.
• [4] P. R. Beesack, Integral inequalities of the Wirtinger type, Duke Math. J. 25, 477-498, (1958).
• [5] P. R. Beesack, Hardy’s inequality and its extensions, Pacific J. Math. 11 (1961), 39–61.
• [6] G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, 1988.
• [7] C. F. Lee, C.C. Yeh, C.H. Hong, R.P. Agarwal, Lyapunov and Wirtinger inequalities, Appl. Math. Lett. 17 (2004) 847–853.
• [8] J. Jaros, On an integral inequality of the Wirtinger type, Applied Mathematics Letters 24 (2011) 1389–1392.
• [9] D. S. Mitrinovic, J.E. Pecaric and A.M. Fink, Inequalities involving functions and their integrals and derivatives, Dordrecht, 1991.
• [10] S-E. Takahasi and T. Miura, A note on Wirtinger-Beesack’s integral inequalities, Math. Inequal. Appl. 6 (2003), no. 2, 277–282.
• [11] C. A. Swanson, Wirtinger’s inequality, SIAM J. Math. Anal. 9, 484-491, (1978).