Analogy of Classical and Dynamic Inequalities Merging on Time Scales

Sahir, Muhammad Jibril Shahab

doi:10.7862/rf.2020.10

Cited by 2 publications

(4 citation statements)

References 8 publications

(12 reference statements)

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“…Replacing, in the preceding inequality, |f (x)| by |f (x)| δ 1 and taking both sides of the inequality to the power 1 δ 2 > 0, we deduce the desired result (14). Now, we state the following extension of reverse Schlömilch's inequality with Specht's ratio on time scales.…”

Section: Resultsmentioning

confidence: 72%

“…The time scales calculus is studied as delta calculus, nabla calculus, and diamond-α calculus. This hybrid theory is also widely applied on dynamic inequalities, see [1,6,12,13,14,15]. The basic work on dynamic inequalities is done by Ravi Agarwal, George Anastassiou, Martin Bohner, Allan Peterson, Donal O'Regan, Samir Saker, and many other authors.…”

Section: Introductionmentioning

confidence: 99%

“…Without loss of generality, we may suppose that b a |w(x)| α x = 1. Therefore, by inequality(14), we have inequality(15).…”

mentioning

confidence: 97%

See 2 more Smart Citations

Specht's ratio and logarithmic mean in time scale dynamic inequalities and their retrospective variants

Afzal

Sahir

2023

ACUTM

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In this research article, we investigate reverse Radon's inequality, reverse Bergström's inequality, the reverse weighted power mean inequality, reverse Schlömilch's inequality, reverse Bernoulli's inequality and reverse Lyapunov's inequality with Specht's ratio on time scales. We also present reverse Rogers--Holder's inequality with logarithmic mean and Specht's ratio on time scales. The time scale dynamic inequalities unify and extend some continuous inequalities and their corresponding discrete and quantum versions.

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Section: Resultsmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

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Specht's ratio and logarithmic mean in time scale dynamic inequalities and their retrospective variants

Afzal

Sahir

2023

ACUTM

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“…This field has a wide scope. Recently, interesting results have obtained by using Specht's ratio and Kantorovich's ratio on time scales as given in [18]. By using these ratios, we can explore further results.…”

mentioning

confidence: 93%

Coordination of Classical and Dynamic Inequalities Complying on Time Scales

Sahir

2023

Eur. J. Math. Anal.

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In this research article, we present extensions of some classical inequalities such as Schweitzer, Pólya–Szegö, Kantorovich and Greub–Rheinboldt inequalities of fractional calculus on time scales. To investigate generalizations of such types of classical inequalities, we use the time scales Riemann–Liouville type fractional integrals. We explore dynamic inequalities on delta calculus and their symmetric nabla versions. A time scale is an arbitrary nonempty closed subset of the real numbers. The theory of time scales is applied to combine results in one comprehensive form. The calculus of time scales unifies and extends continuous versions and their discrete and quantum analogues. By using the calculus of time scales, results are presented in more general form. This hybrid theory is also widely applied on dynamic inequalities.

show abstract

Analogy of Classical and Dynamic Inequalities Merging on Time Scales

Cited by 2 publications

References 8 publications

Specht's ratio and logarithmic mean in time scale dynamic inequalities and their retrospective variants

Specht's ratio and logarithmic mean in time scale dynamic inequalities and their retrospective variants

Coordination of Classical and Dynamic Inequalities Complying on Time Scales

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