Объединение классических и динамических неравенств, возникающих при анализе временных масштабов

In this paper, we present an extension of dynamic Renyi’s inequality on time scales by using the time scale Riemann–Liouville type fractional integral. Furthermore, we find generalizations of the well–known Lyapunov’s inequality and Radon’s inequality on time scales by using the time scale Riemann–Liouville type fractional integrals. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues. В этой статье мы представляем расширение динамического неравенства Реньи на шкалы времени с помощью дробного интеграла типа Римана-Лиувилля. Кроме того, мы находим обобщения хорошо известного неравенства Ляпунова и неравенства Радона на шкалах времени с помощью дробных интегралов типа Римана-Лиувилля на шкале. Наши исследования объединяют и расширяют некоторые непрерывные неравенства и соответствующие им дискретные аналоги.

CONSONANCY OF DYNAMIC INEQUALITIES CORRELATED ON TIME SCALE CALCULUS

In this paper, discrete and continuous versions of some inequalitiessuch as Radon's Inequality, Bergstrom's Inequality, Nesbitt's Inequality,Rogers-Holder's Inequality and Schlomilch's Inequality are unified on dynamictime scale calculus in extended form.

Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus

The aim of this paper is to synthesize discrete and continuous versions of some dynamic inequalities such as Radon’s Inequality, Bergström’s Inequality, Schlömilch’s Inequality and Rogers-Hölder’s Inequality on time scales in comprehensive form.

Consensus of classical and fractional inequalities having congruity on time scale calculus

In this paper, we find accordance of some classical inequalities and fractional dynamic inequalities. We find inequalities such as Radon’s inequality, Bergström’s inequality, Rogers-Hölder’s inequality, Cauchy-Schwarz’s inequality, the weighted power mean inequality and Schlömilch’s inequality in generalized and extended form by using the Riemann-Liouville fractional integrals on time scales.

Dynamic Fractional Inequalities Amplified on Time Scale Calculus Revealing Coalition of Discreteness and Continuity

In this paper, we present a generalization of Radon’s inequality on dynamic time scale calculus, which is widely studied by many authors and an intrinsic inequality. Further, we present the classical Bergström’s inequality and refinement of Nesbitt’s inequality unified on dynamic time scale calculus in extended form.

A refinement of a Radon type inequality

In this paper we prove a refinement of a Radon type inequality, previously considered by authors in [Batinet¸u-Giurgiu, D. M. and Pop, O. T., ˘ A generalization of Radon’s inequality, Creat. Math. Inform., 19 (2010), No. 2, 116–121] and [Batinet¸u-Giurgiu, D. M., M ˘ arghidanu, D. and Pop, O. T., ˘ A new generalization of Radon’s inequality and applications, Creat. Math. Inform., 20 (2011), No. 2, 111–116].

A new generalization of Radon’s Inequality and applications

In this paper we prove a new generalization of Radon’s Inequality and give some applications.