New proofs of some discrete inequalities of Wirtinger’s type

Authors: I. Z. Milovanović, E. I. Milovanović, D. Ć. Dolićanin, T. Z. Mirković

Keywords: Discrete inequalities; Wirtinger inequality

Abstract:

A new approach in proving some well-known inequalities of Wirtinger’ s type is presented in this paper. Proofs are short, elegant and based on one class of inequalities for real numbers.

References:

[1] Agarwal, R.P. (2000) Difference equations and inequalities, theory methods and applications. New York: Marcel Dekker, Inc [2] Bellman, R.E. (1960) Introduction to matrix analysis. New York -Toronto -London: McGraw-Hill Book [3] Erdos, P., Ruderman, H.D., Willey, M., Anning, N. (1935) Problems for Solution: 3739-3743. American Mathematical Monthly, 42(6): 396 [4] Fan, K., Taussky, O., Todd, J. (1955) Discrete analogs of inequalities of Wirtinger. Monatshefte für Mathematik, 59(2): 73-90 [5] Lenhard, H.-Christof (1961) Verallgemeinerung und Verschärfung der Erdös-Mordellschen Ungleichung für Polygone. Archiv der Mathematik, 12(1): 311-314 [6] Milovanovic, G.V., Milovanovic, I.Z. (1982) On discrete inequalities of Wirtinger’s type. Journal of Mathematical Analysis and Applications, 88(2): 378-387 [7] Milovanović, G.V., Milovanović, I.Ž. (1984) Some discrete inequality of Opial’s type. Acta Sci. Math. (Szeged), 413-417; 47 [8] Milovanović, G.V., Milovanović, I.Ž. (1978) Disrete inequalities of Wirtingers type, Recent Progress in Inequalities: A Volume dedicated to Profesor D. S. Mitrinović (1908-1995). u: Milovanović G.V. [ur.] Dordrecht: Kluwer, 289-308 [9] Mitrinović, D.S., Pečarić, J.E., Funk, A.M. (1993) Classical and new inequalities in analysis. Dordrecht: Kluwer Academic Publications [10] Mitrinović, D.S., Pečarić, J.E., Volenec, V. (1989) Recent advances in geometric inequalities. Dordrecht: Kluwer Academic Publishers [11] Mordell, L.J., Barrow, D.F. (1937) Solution of problem 370. American Mathematical Monthly, 44(4): 252 [12] Ozeki, N. (1957) On P. Erdös inequality for the triangle. J. College Arts Sci. Chiba Univ, 2, 247-250 [13] Wolstenholme, J. (1867) A book of mathematical problems. Cambridge-London [14] Wu, S., Debnath, L. (2007) Generalization of the Wolstenholme cyclic inequality and its application. Computers & Mathematics with Applications, 53(1): 104-114 [15] Xiao, Z.G., Zhang, Z.H. (2005) A simple new proof of Fan-Taussky-Todd inequalities. Australian J. Math. Anal. Appl, vol. 2, 1, 1-5