Improvements of Jensen-Type Inequalities for Diamond-α Integrals
نویسندگان
چکیده
We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left-hand side and the right-hand side of these inequalities and present several families of functions for which these results can be applied.
منابع مشابه
New Jensen and Ostrowski Type Inequalities for General Lebesgue Integral with Applications
Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.
متن کاملGeneral Minkowski type and related inequalities for seminormed fuzzy integrals
Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.
متن کاملOn Generalizations of Hadamard Inequalities for Fractional Integrals
Fej'{e}r Hadamard inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r Hadamard inequalities for $k$-fractional integrals. We deduce Fej'{e}r Hadamard-type inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.
متن کاملSymmetric Rogers-Hölder's inequalities on diamond-α calculus
We present symmetric Rogers--Hölder's inequalities on time scales when $frac{1}{p}+frac{1}{q}+frac{1}{r}=0$ and $frac{r}{p}+frac{r}{q}$ is not necessarily equal to $1$ where $p,$ $q$ and $r$ are nonzero real numbers.
متن کاملGeneralization of the Lyapunov type inequality for pseudo-integrals
We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ ; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...
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:
دوره 2014 شماره
صفحات -
تاریخ انتشار 2014