A new Hilbert-type integral inequality and the equivalent form
نویسندگان
چکیده
We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered.
منابع مشابه
General Hardy-Type Inequalities with Non-conjugate Exponents
We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...
متن کاملAn extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel
In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.
متن کاملOn 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 more accurate multiple Hilbert-type inequality
By using Euler-Maclaurin's summation formula and the way of real analysis, a more accurate multipleHilbert-type inequality and the equivalent form are given. We also prove that the same constantfactor in the equivalent inequalities is the best possible.
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 کاملOn a Hardy-Hilbert-Type Inequality with a General Homogeneous Kernel
By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.
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 2006 شماره
صفحات -
تاریخ انتشار 2006