Quadratic refinements of Young type inequalities
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DOI: 10.1515/ms-2017-0416
Abstract: Abstract In this paper, we mainly give some quadratic refinements of Young type inequalities. Namely: (va+(1−v)b)2−v∑j=1N2j(b−ab2j−12j)2≤(avb1−v)2+v2(a−b)2 $$\begin{array}{} \displaystyle (va+(1-v)b)^{2}-v{{\sum\limits_{j=1}^N}}2^{j}\Big(b- \sqrt[2^{j}]{ab^{2^{j}-1} }\, \Big)^{2}\leq(a^{v}b^{1-v})^{2}+v^{2}(a-b)^{2} \end{array}$$ for v ∉ [0, 12N+1 $\begin{array}{} \displaystyle \frac{1}{2^{N+1}} \end{array}$], N ∈ ℕ,… read more here.
Keywords: begin array; array; young type; refinements young ... See more keywords