On two bivariate elliptic means
نویسندگان
چکیده
منابع مشابه
On Two Bivariate Elliptic Means
This paper deals with the inequalities involving the Schwab-Borchardt mean SB and a new mean N introduced recently by this author. In particular optimal bounds, for SB are obtained. Inequalities involving quotients N/SB , for the data satisfying certain monotonicity conditions, are derived. Mathematics subject classification (2010): 26E60, 26D05.
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A new family of bivariate means is defined and investigated. Members of that family are generated by the Schwab-Borchardt mean. Comparison results involving new means and the second Neuman mean are established. In particular, two means introduced and studied by J. Sándor and Z. Yang belong to a new class of means.
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Sharp companion inequalities for certain bivariate means are obtained. In particular, companion inequalities for those discovered by Stolarsky and Sándor are established.
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A one-parameter family of bivariate means is introduced. Members of the new family of means are derived from a bivariate symmetric mean. It is shown that new means are symmetric in their variables. Several inequalities involving parametric versions of two Seiffert means, the Neuman-Sándor mean, and the logarithmic means are obtained. It is shown that the last four means belong to the family of ...
متن کاملAn Optimal Inequalities Chain for Bivariate Means
Abstract. Let p ∈ R , M be a bivariate mean, and Mp be defined by Mp(a,b) = M1/p(ap,bp) (p = 0) and M0(a,b) = limp→0 Mp(a,b) . In this paper, we prove that the sharp inequalities L2(a,b) < P(a,b) < NS1/2(a,b) < He(a,b) < A2/3(a,b) < I(a,b) < Z1/3(a,b) < Y1/2(a,b) hold for all a,b > 0 with a = b , where L(a,b) = (a− b)/(loga − logb) , P(a,b) = (a− b)/[2arcsin((a−b)/(a+b))] , NS(a,b) = (a−b)/[2ar...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2017
ISSN: 1846-579X
DOI: 10.7153/jmi-11-30