scholarly journals CONSONANCY OF DYNAMIC INEQUALITIES CORRELATED ON TIME SCALE CALCULUS

2020 ◽  
Vol 51 (3) ◽  
pp. 233-243
Author(s):  
Muhammad Jibril Shahab Sahir
Keyword(s):  
Time Scale ◽  
Hölder’S Inequality ◽  
Extended Form ◽  
Hölder's Inequality ◽  
Time Scale Calculus ◽  
Radon’S Inequality

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.

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

2019 ◽  
Vol 27 (1) ◽  
pp. 57-69
Author(s):  
Muhammad Jibril Shahab Sahir
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Fractional Integrals ◽  
Power Mean ◽  
Extended Form ◽  
Hölder's Inequality ◽  
Time Scale Calculus ◽  
Power Mean Inequality ◽  
Radon’S Inequality

Abstract 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.

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

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Muhammad Jibril Shahab Sahir
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Time Scale Calculus ◽  
Radon’S Inequality

AbstractThe 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.

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

2018 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
Muhammad Sahir
Keyword(s):  
Time Scale ◽  
Extended Form ◽  
Time Scale Calculus ◽  
Dynamic Time ◽  
Radon’S Inequality

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.

scholarly journals Hilbert-type inequalities for time scale nabla calculus

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
H. M. Rezk ◽  
Ghada AlNemer ◽  
H. A. Abd El-Hamid ◽  
Abdel-Haleem Abdel-Aty ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Arbitrary Time ◽  
Hilbert Type

Abstract This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

scholarly journals More on Hölder’s Inequality and It’s Reverse via the Diamond-Alpha Integral

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1716
Author(s):  
M. Zakarya ◽  
H. A. Abd El-Hamid ◽  
Ghada AlNemer ◽  
H. M. Rezk
Keyword(s):  
Linear Combination ◽  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Special Cases ◽  
General Time

In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when T=R.

scholarly journals Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 434 ◽  
Author(s):  
Samir Saker ◽  
Mohammed Kenawy ◽  
Ghada AlNemer ◽  
Mohammed Zakarya
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Chain Rule ◽  
Hölder's Inequality ◽  
Conformable Calculus

In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When α = 1 we obtain some well-known time-scale inequalities due to Hardy, Copson, Bennett and Leindler inequalities.

scholarly journals When to Spray: a Time-Scale Calculus Approach to Controlling the Impact of West Nile Virus

2009 ◽  
Vol 14 (2) ◽  
Author(s):  
Diana Thomas ◽  
Marion Weedermann ◽  
Lora Billings ◽  
Joan Hoffacker ◽  
Robert A. Washington-Allen
Keyword(s):  
West Nile Virus ◽  
Time Scale ◽  
West Nile ◽  
Time Scale Calculus ◽  
The Impact

scholarly journals Объединение классических и динамических неравенств, возникающих при анализе временных масштабов

2020 ◽  
pp. 26-36
Author(s):  
M.J.S. Sahir
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Lyapunov’S Inequality ◽  
Discrete Analogues ◽  
Radon’S Inequality

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.

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