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In this paper, we present sharp bounds for the two Neuman means S HA and S CA derived from the Schwab-Borchardt mean in terms of convex combinations of either the weighted arithmetic and geometric means or the weighted arithmetic and quadratic means, and the mean generated either by the geometric or by the quadratic mean.
In the article, we provide a monotonicity rule for the function [Formula: see text], where [Formula: see text] is a positive differentiable and decreasing function defined on [Formula: see text] ([Formula: see text]), and [Formula: see text] and [Formula: see text] are two real power series converging on [Formula: see text] such that the sequence [Formula:… (More)
distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In the paper, we find the greatest values α 1 , α 2 , α 3 , α 4 and the least values β 1 , β 2 , β 3 , β 4 such that the double inequalities α 1 A(a, b) + (1 − α… (More)
In this paper, we present the sharp upper and lower bounds for the Neuman means S AC and S CA in terms of the the arithmetic mean A and contraharmonic mean C. The given results are the improvements of some known results.