Geodesic
Wirtinger's Inequalities on Time Scales
Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 161-171

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DOI

This paper is devoted to the study of Wirtinger-type inequalities for the Lebesgue $\Delta$ -integral on an arbitrary time scale $\mathbb{T}$ . We prove a general inequality for a class of absolutely continuous functions on closed subintervals of an adequate subset of $\mathbb{T}$ . By using this expression and by assuming that $\mathbb{T}$ is bounded, we deduce that a general inequality is valid for every absolutely continuous function on $\mathbb{T}$ such that its $\Delta$ -derivative belongs to $L_{\Delta }^{2}\,([a,\,b)\,\cap \,\mathbb{T})$ and at most it vanishes on the boundary of $\mathbb{T}$ .
DOI : 10.4153/CMB-2008-018-6
Mots-clés : 39A10, time scales calculus, Δ-integral, Wirtinger's inequality 
Agarwal, Ravi P.; Otero-Espinar, Victoria; Perera, Kanishka; Vivero, Dolores R. Wirtinger's Inequalities on Time Scales. Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 161-171. doi: 10.4153/CMB-2008-018-6
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     title = {Wirtinger's {Inequalities} on {Time} {Scales}},
     journal = {Canadian mathematical bulletin},
     pages = {161--171},
     year = {2008},
     volume = {51},
     number = {2},
     doi = {10.4153/CMB-2008-018-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-018-6/}
}
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