Some Steffensen-type dynamic inequalities on time scales

El‐Deeb, Ahmed A.; El-Sennary, H. A.; Khan, Zareen A.

doi:10.1186/s13662-019-2193-2

Cited by 18 publications

(16 citation statements)

References 20 publications

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“…If T = R, Theorem 3.10 reduces to the corresponding result from [15]. Moreover, in the case of the Lebesgue scale measure ∆t, we arrive at the result established in [11].…”

Section: Remark 33supporting

confidence: 60%

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Some Steffensen-type inequalities over time scale measure spaces

El‐Deeb

Krnić

2020

Filomat

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In this paper we study some new dynamic Steffensen-type inequalities on a general time scale. More precisely, we deal with time scale spaces with positive ?-finite measures. As an application, our results are compared with some previous results known from the literature. It turns out that our results generalize some previously known Steffensen-type inequalities in a classical setting.

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“…If T = R, Theorem 3.10 reduces to the corresponding result from [15]. Moreover, in the case of the Lebesgue scale measure ∆t, we arrive at the result established in [11].…”

Section: Remark 33supporting

confidence: 60%

“…Remark 3.13. It should be noted here that Theorem 3.12 is an extension of the corresponding results derived in [11] and [15].…”

Section: Remark 33supporting

confidence: 54%

Some Steffensen-type inequalities over time scale measure spaces

El‐Deeb

Krnić

2020

Filomat

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“…and (49) Then as in the proof of previous theorem from (46) we see that the inequalities (25) and (26) hold for v 2 . From (50), (26) and the hypothesis (45).…”

supporting

confidence: 59%

“…Then as in the proof of Theorem 3.4, from (34). We see that the inequalities (25) and (26) hold for v 1 . By differentiating (38) and by using Lemma 3.3, we deduce…”

Section: Lemma 32 ([34]mentioning

confidence: 57%

“…The book on the subject of time scales by Bohner and Peterson [14] summarizes and organizes much of time scale calculus. During the past decade a number of dynamic inequalities have been established by some authors which are motivated by some applications, for example, when studying the behavior of solutions of certain class of dynamic equations on a time scale T. We refer the reader to [5,8,9,14,16,22,23,24,25,26,35,36,37,38,48,49,50] for contributions, and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

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On some generalizations of nonlinear dynamic inequalities on time scales and their applications

2019

Appl Anal Discrete Math

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In this article, by using Young's inequality, we prove some new nonlinear dynamic inequalities of Gronwall-Bellman-Pachpatte type on time scales. These inequalities give us the integral and discrete version, and also extend some known dynamic inequalities in certain papers. We can also say, the inequalities proved in this paper can be used as handy tools in the study of qualitative properties of some dynamic equations on time scales. Some examples are introduced to demonstrate the applications of these inequalities.

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Diamond alpha Bennett‐Leindler type dynamic inequalities and their applications

Kayar

Kaymakçalan

Pelen

2021

Math Methods in App Sciences

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In this paper, two kinds of dynamic Bennett-Leindler type inequalities via the diamond alpha integrals are derived. The first kind consists of eight new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together due to the fact that convex linear combinations of delta and nabla Bennett-Leindler type inequalities give diamond alpha Bennett-Leindler type inequalities. The second kind involves four new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Bennett-Leindler type inequalities. For the second type, choosing 𝛼 = 1 or 𝛼 = 0 not only yields the same results as the ones obtained for delta and nabla cases but also provides novel results for them.Therefore, both kinds of our results expand some of the known delta and nabla Bennett-Leindler type inequalities, offer new types of these inequalities, and bind and unify them into one diamond alpha Bennett-Leindler type inequalities.Moreover, an application of dynamic Bennett-Leindler type inequalities to the oscillation theory of the second-order half linear dynamic equation is developed and presented for the first time ever.

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Some Steffensen-type dynamic inequalities on time scales

Cited by 18 publications

References 20 publications

Some Steffensen-type inequalities over time scale measure spaces

Some Steffensen-type inequalities over time scale measure spaces

On some generalizations of nonlinear dynamic inequalities on time scales and their applications

Diamond alpha Bennett‐Leindler type dynamic inequalities and their applications

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