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 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 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 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 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.

scholarly journals Some Dynamic Inequalities via Diamond Integrals for Function of Several Variables

2021 ◽  
Vol 5 (4) ◽  
pp. 207
Author(s):  
Muhammad Bilal ◽  
Khuram Ali Khan ◽  
Hijaz Ahmad ◽  
Ammara Nosheen ◽  
Khalid Mahmood Awan ◽  
...  
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Jensen’S Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Several Variables ◽  
Time Scale Calculus ◽  
Special Cases ◽  
Function Of Several Variables ◽  
New Inequalities

In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals of time scale calculus. These extensions are used to generalize Hardy-type inequalities with general kernels via diamond integrals for the function of several variables. Some Hardy Hilbert and Polya Knop type inequalities are also discussed as special cases. Classical and new inequalities are deduced from the main results using special kernels and particular time scales.

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