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Using Hayashi's inequality, an Iyengar type inequality for functions with bounded second derivative is obtained. This result improves a similar result from [N. Elezovi´c, J. Pečari´c, Steffensen's inequality and estimates of error in trapezoidal rule, Appl. In 1938 Iyengar proved the following inequality in [1]: Theorem 1. Let function f be differentiable… (More)

- Vera Čuljak, Iva Franjić, Roqia Ghulam, Josip Pečarić, Matti K. Vuorinen
- 2011

The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published results is established, and some applications of the extended… (More)

- Iva Franjić, Sadia Khalid, Josip Pečarić
- 2011

In this paper, we extend some old and give some new refinements of the Jensen-Steffensen inequality. Further, we investigate the log-convexity and the exponential convexity of functionals defined via these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the… (More)

- I. FRANJIĆ, J. PEČARIĆ
- 2009

Inequalities estimating the absolute value of the difference between the integral and the quadrature, i.e. the Dragomir-Agarwal-type inequalities, are given for the general 3, 4 and 5-point quadrature formulae, both classical and corrected. Beside values of the function in the chosen nodes, "corrected" quadrature formula includes values of the first… (More)

The aim of this paper is to generalize inequality f ðxÞ À 1 b À a

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