A NOTE ON COPSON'S INEQUALITY INVOLVING SERIES OF POSITIVE TERMS
Main Article Content
In the present note we establish some generalizations of Copson's inequality concerning series of positive tenns. The method used in the proofs is elementary and our results provide new estimates on inequalities of this type.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
E. F . Beckenbach and R. Bellman, "Inequalities ', Springer-Verlag-Berlin, New York, 1965.
E. T. Copson, Note on a series of positive terms, J. London Math. Soc. 2 (1927), 9-12.
E. B. Elliott, A simple exposition of some recently proved facts as to convergency, J. London Math. Soc. 1 (1926), 93-96.
G. H. Hardy, Note on a theorem of Hilbert, Math. Zeitschr 6 (1920), 314-317.
G. H. Hardy, Remarks on three recent notes in the Journal, J. London Math. Soc. 3 (1928), 166-169.
G. H. Hardy, "Divergent series," Cambridge, 1948.
G. H. Hardy, J. E. Littlewood and G. Polya, "lneqalities," Cambridge University Press, 1934.
M. lzumi, S. lzumi and G. Peterson, On Hardy's inequality and its generalization, Tohoku Math. Jour. 21 (1969), 601-613.
P. D. Johnson JR. and R. N. Mohapatra, Inequalities involving lower triangular matrices, Proc. London Math. Soc. 41 (1980), 83-137.
} A. Kufner, O. John and S. Fucik, "Function spaces," Noordhoff International Publishing, Leyden, 1977.
E. Landau, A note on a theorem concerning series of positive terms, J. London Math. Soc. 1 (1926), 38-39.
C. S. Lee, On some generalizations of inequalities of Opial, Yang and Shum, Canad. Math. Bull. 23 (1980), 71-80.
E. R. Love, Generalizations of Hardy's and Copson's inequalities, J. London Math. Soc. 30 (1984), 431-440.
D. S. Mitrinovic, "Analytic Inequalities," Spring-Verlag-Berlin, New York, 1970.
B. G. Pachpatte, On a new class of Hardy type inequalities, Proc. Royal Soc. Edinburgh 105A (1987), 265-274.
G. M. Petersen, An inequality of Hardy's, Quart. J. Math. Oxford 13 (1962), 237-240.