Affiliation:
1. Department of Information Engineering, Weihai Vocational College, Weihai City, Shandong Province, China
2. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China + Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin City, China
Abstract
In the paper, the authors discover the best constants ?1, ?2, ?1, and ?2 for
the double inequalities ?1C(a,b) + (1-?1)A(a,b) < T(a,b) < ?1C(a,b) +
(1-?1)A(a,b) and ?2/A(a,b) + 1-?2/C(a,b) < 1/T(a,b) < ?2/A(a,b) +
1-?2-C(a,b) to be valid for all a, b > 0 with a ? b, where C(a,b) =
2(a2+ab+b2)/3(a+b), A(a,b) = a+b/2, and T(a,b) = 2/???2,0 ?a2 cos2 ? + b2 sin2 ? d ?
are respectively the centroidal, arithmetic, and
Toader means of two positive numbers a and b. As an application of the above
inequalities, the authors also find some new bounds for the complete
elliptic integral of the second kind.
Publisher
National Library of Serbia
Cited by
23 articles.
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