The Best Constants for a Double Inequality in a Triangle
نویسندگان
چکیده
In this short note, by using some of Chen’s theorems and classic analysis, we obtain a double inequality for triangle and give a positive answer to a problem posed by Yang and Yin [6].
منابع مشابه
On the metric triangle inequality
A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.
متن کاملRefined quadratic estimations of Shafer’s inequality
We establish an inequality by quadratic estimations; the double inequality [Formula: see text] holds for [Formula: see text], where the constants [Formula: see text] and 32 are the best possible.
متن کاملAn Analysis of ‘Triangle Ordering’ in Foreign Exchange Market (Forex): Simultaneous Ordering of Three Major Currency Pairs
With considering a ‘triangle of three major currency pairs’, there is a tiny difference between multiplication of exchange rate for the first two currency pairs and the third. To discover whether this little difference can lead to a neutral arbitrage or not, I took portfolios of 35 baskets of three major currency pairs(combinations of all 7 major currencies). There are eight approaches (differe...
متن کاملA Sharp Double Inequality for the Inverse Tangent Function
The inverse tangent function can be bounded by different inequalities, for example by Shafer’s inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent function. In particular, we sharpen Shafer’s inequality and calculate the best corresponding constants. The maximum relative errors of the obtained bounds are ap...
متن کاملA more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function
By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008