Extensions of certain integral inequalities on time scales

نویسندگان

  • Umut Mutlu Özkan
  • Mehmet Zeki Sarikaya
  • Hüseyin Yildirim
چکیده

In this work, we establish Hölder’s inequality, Minkowski’s inequality and Jensen’s inequality on time scales via the nabla integral and diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals. c © 2008 Published by Elsevier Ltd

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Some New Delay Integral Inequalities in Two Independent Variables on Time Scales

Some new Gronwall-Bellman type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete anal...

متن کامل

Research Article Some Nonlinear Integral Inequalities on Time Scales

The theory of time scales was introduced by Hilger [1] in his Ph.D. thesis in 1988 in order to unify continuous and discrete analysis. Recently, many authors have extended some fundamental integral inequalities used in the theory of differential and integral equations on time scales. For example, we refer the reader to the literatures [2–8] and the references cited therein. In this paper, we in...

متن کامل

Bounds for Certain Delay Integral Inequalities on Time Scales

The unification and extension of differential equations, difference equations, q-difference equations, and so on to the encompassing theory of dynamic equations on time scales was initiated by Hilger 1 in his Ph.D. thesis in 1988. During the last few years, some integral inequalities on time scales related to certain inequalities arising in the theory of dynamic equations had been established b...

متن کامل

Symmetric 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 کامل

A class of retarded Volterra-Fredholm type integral inequalities on time scales and their applications

*Correspondence: [email protected] School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P.R. China Abstract In this paper, we study some new retarded Volterra-Fredholm type integral inequalities on time scales, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as tools in the qualitative theory ...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Appl. Math. Lett.

دوره 21  شماره 

صفحات  -

تاریخ انتشار 2008