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In this paper, we prove that λ = 1/2− √ 1− e−2/p/2 and μ = 1/2−√6p/(6p) are the best possible parameters on the interval (0,1/2) such that the double inequalities… Click to show full abstract
In this paper, we prove that λ = 1/2− √ 1− e−2/p/2 and μ = 1/2−√6p/(6p) are the best possible parameters on the interval (0,1/2) such that the double inequalities G [λa+(1−λ)b,λb+(1−λ )a]A1−p (a,b) < X (a,b) < Gp [μa+(1−μ)b,μb+(1−μ)a]A1−p (a,b) hold for all p ∈ [1,∞) and a,b > 0 with a = b , where G(a,b) is the geometric mean, A(a,b) is the arithmetic mean, and X (a,b) is the Sándor mean. Mathematics subject classification (2020): 26E60.
Keywords:
terms combination;
combination geometric;
bounds ndor;
optimal bounds;
ndor mean;
mean terms
Journal Title: Journal of Mathematical Inequalities
Year Published: 2021
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Journal Title: Journal of Mathematical Inequalities
Year Published: 2021
Link to full text (if available)
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recommendations!