A unified approach to several inequalities involving functions and derivatives

Javier Duoandikoetxea

Displaying similar documents to “A unified approach to several inequalities involving functions and derivatives”

Some generalized error inequalities and applications.

Zafar, Fiza, Mir, Nazir Ahmad (2008)

Journal of Inequalities and Applications [electronic only]

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Asymptotic expressions for remainder terms of some quadrature rules

Nenad Ujević, Nataša Bilić (2008)

Open Mathematics

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Asymptotic expressions for remainder terms of the mid-point, trapezoid and Simpson’s rules are given. Corresponding formulas with finite sums are also given.

Inequalities for the Riemann–Stieltjes Integral of under the Chord Functions with Applications

Silvestru S. Dragomir (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We say that the function $f : [a, b] \to ℝ$ is under the chord if $\frac{(b - t) f (a) + (t - a) f (b)}{b - a} \geq f (t)$ for any $t \in [a, b]$ . In this paper we proved amongst other that $\int_{a}^{b} u (t) d f (t) \geq \frac{f (b) - f (a)}{b - a} \int_{a}^{b} u (t) d t$ provided that $u : [a, b] \to ℝ$ is monotonic nondecreasing and $f : [a, b] \to ℝ$ is continuous and under the chord. Some particular cases for the weighted integrals in connection with the Fejér inequalities are provided. Applications for continuous functions of selfadjoint operators on Hilbert spaces are also given.