SHARP BOUNDS FOR SANDOR-YANG MEANS IN TERMS OF ONE-PARAMETER FAMILY OF BIVARIATE MEANS

In the article, we present the best possible parameters alpha(1), alpha(2), alpha(3), alpha(4), beta(1), beta(2), beta(3) and beta(4) on the interval (0, 1) such that the double inequalities G(alpha 1)(x,y) < R-GQ(x,y) < G(beta 1)(x,y), Q(alpha 2)(x,y) < R-QG(x,y) < Q(beta 2)(x,y), H-alpha 3(x,y) < R-GQ(x,y) < H-beta 3(x,y), C-alpha 4(x,y) < R-QG(x,y) < C-beta 4(x,y) hold for all x,y > 0 with x not equal y, where R-GQ(x,y) and R-QG(x,y) arc the Sandor-Yang means, H-p(x,y), G(p) (x,y), Q(p)(x,y) and C-p(x,y) are the one-parameter means.