Hermite-Hadamard's Inequality on Time Scales
نویسندگان
چکیده
We establish several Hermite-Hadamard’s inequalities on time scales. One of these results says as follows: Suppose that (1) f a b R : [ , ]® is convex; (2) p q p q , (0,1), = 1 ∈ + ; g C a b R rd ∈ + ([ , ], ) is symmetric with respect to x pa qb = + = : x on [ , ] a b , i.e., g qt g pt t b a ( ) = ( ), [0, ], x x − + ∀ ∈ − then:
منابع مشابه
Hermite-Hadamard's type inequalities for operator convex functions
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we give a simple proof and a new generalization of the Hermite-Hadamard inequality for operator convex functions.
متن کاملOn a reverse Mulholland’s inequality in the whole plane
By introducing multi-parameters, applying the weight coefficients and Hermite-Hadamard's inequality, we give a reverse of the extended Mulholland inequality in the whole plane with the best possible constant factor. The equivalent forms and a few particular cases are also considered.
متن کاملOn a more accurate Hardy-Mulholland-type inequality
By using the way of weight coefficients, the technique of real analysis, and Hermite-Hadamard's inequality, a more accurate Hardy-Mulholland-type inequality with multi-parameters and a best possible constant factor is given. The equivalent forms, the reverses, the operator expressions and some particular cases are considered.
متن کاملA Weighted Hermite Hadamard Inequality for Steffensen–Popoviciu and Hermite–Hadamard Weights on Time Scales
In this paper, we present a weighted version of the Hermite–Hadamard inequality for convex functions on time scales, with weights that are allowed to take some negative values, these are the Steffensen–Popoviciu and the Hermite–Hadamard weights. We also present some applications of this inequality.
متن کاملOn a more accurate half-discrete Hardy–Hilbert-type inequality related to the kernel of arc tangent function
By means of weight functions and Hermite-Hadamard's inequality, and introducing a discrete interval variable, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of arc tangent function and a best possible constant factor is given, which is an extension of a published result. The equivalent forms and the operator expressions 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
عنوان ژورنال:
- IJALR
دوره 2 شماره
صفحات -
تاریخ انتشار 2011