On Hilbert's Inequality for Double Series and Its Applications
نویسندگان
چکیده
This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u x and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHp function are given.
منابع مشابه
On a New Reverse Hilbert\'s Type Inequality
In this paper, by using the Euler-Maclaurin expansion for the Riemann-$zeta$ function, we establish an inequality of a weight coefficient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.
متن کاملOn a decomposition of Hardy--Hilbert's type inequality
In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.
متن کاملOn Further Analogs of Hilbert's Inequality
By introducing the function | lnx − ln y|/(x + y + |x − y|), we establish new inequalities similar to Hilbert's type inequality for integrals. As applications, we give its equivalent form as well.
متن کاملOn Hilbert’s Inequality for Double Series and Its Applications
This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u x and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHp function are given.
متن کاملOn the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications
In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2008 شماره
صفحات -
تاریخ انتشار 2008