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A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications

Mohammad W. Alomari (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral [...] ∫abf(t) du(t) a b f ( t ) d u ( t ) , where f is assumed to be of r-H-Hölder type on [a, b] and u is of bounded variation on [a, b], is proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.

Characterization of intermediate values of the triangle inequality II

Hiroki Sano, Tamotsu Izumida, Ken-Ichi Mitani, Tomoyoshi Ohwada, Kichi-Suke Saito (2014)

Open Mathematics

In [Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035] there was established a norm inequality which characterizes all intermediate values of the triangle inequality, i.e. C n that satisfy 0 ≤ C n ≤ Σj=1n ‖x j‖ − ‖Σj=1n x j‖, x 1,...,x n ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.

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