Abstract In this paper, we establish Jensen’s inequality for s -convex functions in the first sense. By using inequalities, obtain some Cauchy type means p and Also, by Hermite–Hadamard inequalities respective generalized convex functions, find new means.

In this paper we present an online unsupervised method based on clustering to find defects in concrete structures using hammering. First, the initial dataset of sound samples is roughly clustered using the k-means algorithm with the k-means++ seeding procedure in order to find the cluster best representative of the structure. Then the regular model for the hammering sound, the centroid of this ...

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Let us consider the logarithmic mean L; the identric mean I; the trigonometric means P and T de…ned by H. J. Sei¤ert, the hyperbolic mean M de…ned by E. Neuman and J. Sándor, and the Gini mean J . The optimal estimations of these means by power means Ap and also some of the optimal estimations by Lehmer means Lq are known. We prove two new optimal estimation by Lehmer means L0 < M < L1=6 and L1...