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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)
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)
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)
and Applied Analysis 3 where Pj j ∑ i 1 pi, j 1, . . . , n. 1.7 Lemma 1.6. Let f be a convex function on I, p a positive n-tuple such that Pn ∑n i 1 pi 1 and x1, x2, . . . , xn ∈ I, n ≥ 3 such that x1 ≤ x2 ≤ · · · ≤ xn. For fixed x1, x2, . . . , xk, where k 2, 3, . . . , n− 1, the Jensen functional J x,p, f defined in 1.2 is minimal when xk xk 1 · · · xn−1(More)
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