A CLASS OF DOUBLE INEQUALITIES FOR STOLARSKY MEANS
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Let Er,s(a, b) be the Stolarsky mean of the numbers a, b > 0 with parameters r, s ∈ R. We prove that the inequality EL(r,s),L(r,s)(a, b) ≤ Er,s(a, b) ≤ EA(r,s),A(r,s)(a, b) holds for any positive real numbers r, s, a, b, where L(r, s) and A(r, s) are the logarithmic and arithmetic means of the numbers r, s > 0, respectively. Fi- nally, two open problems are proposed.
Abstract
Let Er,s(a, b) be the Stolarsky mean of the numbers a, b > 0 with parameters r, s ∈ R. We prove that the inequality EL(r,s),L(r,s)(a, b) ≤ Er,s(a, b) ≤ EA(r,s),A(r,s)(a, b) holds for any positive real numbers r, s, a, b, where L(r, s) and A(r, s) are the logarithmic and arithmetic means of the numbers r, s > 0, respectively. Fi- nally, two open problems are proposed.
참고문헌 (13)
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