Consonancy of dynamic inequalities correlated on time scale calculus
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Abstract
In this paper, discrete and continuous versions of some inequalities
such as Radon's Inequality, Bergstrom's Inequality, Nesbitt's Inequality,
Rogers-Holder's Inequality and Schlomilch's Inequality are unified on dynamic
time scale calculus in extended form.
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References
R.P. Agarwal, D. O'Regan and S.H. Saker, Dynamic inequalities on time scales, Springer
International Publishing, Cham, Switzerland, (2014).
D. Anderson, J. Bullock, L. Erbe, A. Peterson and H. Tran, Nabla dynamic equations on
time scales, Pan-American Mathematical Journal, 13(1), 1-48, (2003).
E.F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, Gottingen and Heidelberg,
(1961).
R. Bellman, Notes on matrix theory-IV (An inequality due to Bergstrom), Amer. Math.
Monthly, 62, 172-173, (1955).[5] H. Bergstrom, A triangle inequality for matrices, Den Elfte Skandinaviske Matematikerkongress,
(1949), Trodheim, Johan Grundt Tanums Forlag, Oslo, 264-267, (1952).
M. Bohner and A. Peterson, Dynamic equations on time scales, Birkhauser Boston Inc.,
Boston, MA, (2001).
M. Bohner and A. Peterson, Advances in dynamic equations on time scales, Birkhauser
Boston, Boston, MA, (2003).
D.M.B. Giurgiu, D. Marghidanu and O.T. Pop, A new generalization of Radon's Inequality
and applications, Creative Math & Inf, 20(2), 111-116, (2011).
D.M.B. Giurgiu and N. Stanciu, One inequality and some applications, Journal of Science
and Arts, 2(23), 131-134, (2013).
G.H. Hardy, J.E. Littlewood and G. Polya, Inequalities, 2nd ed, Cambridge, University Press,
(1952).
S. Hilger, Ein Makettenkalkul mit Anwendung auf Zentrumsmannigfaltigkeiten, PhD thesis,
Universitat Wurzburg, (1988).
D.S. Mitrinovic, Analytic inequalities, Springer-Verlag, Berlin, (1970).
A. M. Nesbitt, Problem 15114, Educational Times, 3, 37-38, (1903).
U.M. Ozkan, M.Z. Sarikaya and H. Yildirim, Extensions of certain integral inequalities on
time scales, Applied Mathematics Letters, 993-1000, 21, (2008).
J. Radon, Theorie und Anwendungen der absolut additiven Mengenfunktionen, Sitzungsber.
Acad. Wissen. Wien, 122, 1295-1438, (1913).
M.J.S. Sahir, Dynamic inequalities for convex functions harmonized on time scales, Journal
of Applied Mathematics and Pysics, 5, 2360-2370, (2017).
M.J.S. Sahir, Formation of versions of some dynamic inequalities unied on time scale calculus,
Ural Mathematical Journal, 4(2), 88-98, (2018).
Q. Sheng, M. Fadag, J. Henderson and J.M. Davis, An exploration of combined dynamic
derivatives on time scales and their applications, Nonlinear Anal. Real World Appl. 7, 395-
, (2006).