• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.635-647
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• 2014

In this paper, a generalized perturbed midpoint rule is established. Various error bounds for this generalization are also obtained.

• 대한수학회보
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• 제47권2호
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• pp.221-229
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• 2010

Some new $\check{C}$eby$\check{s}$ev type inequalities have been developed by working on functions whose first derivatives are absolutely continuous and the second derivatives belong to the usual Lebesgue space $L_{\infty}[a,\;b]$. A unified treatment of the special cases is also given.

• 대한수학회지
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• 제51권4호
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• pp.791-815
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• 2014

We show amongst other that if $f,g:[a,b]{\rightarrow}\mathbb{C}$ are two functions of bounded variation and such that the Riemann-Stieltjes integral $\int_a^bf(t)dg(t)$ exists, then for any continuous functions $h:[a,b]{\rightarrow}\mathbb{C}$, the Riemann-Stieltjes integral $\int_{a}^{b}h(t)d(f(t)g(t))$ exists and $${\int}_a^bh(t)d(f(t)g(t))={\int}_a^bh(t)f(t)d(g(t))+{\int}_a^bh(t)g(t)d(f(t))$$. Using this identity we then provide sharp upper bounds for the quantity $$\|\int_a^bh(t)d(f(t)g(t))\|$$ and apply them for trapezoid and Ostrowski type inequalities. Some applications for continuous functions of selfadjoint operators on complex Hilbert spaces are given as well.

• 대한수학회보
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• 제49권4호
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• pp.775-785
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• 2012

Some errors in literatures are pointed out and corrected. A generalization of Ostrowski type inequalities for functions whose derivatives in absolute value are s-convex in the second sense is established. Special cases are discussed.