Converses of Copson's inequalities on time scales

Saker, S. H.; 'Regan, Donal; Agarwal, Ravi P.

doi:10.7153/mia-18-18

Cited by 10 publications

(18 citation statements)

References 15 publications

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“…By the following theorem, the reverse of the Bennett's (or Leindler's) inequality ( 7) is unified in Saker et al 34 for the delta time scale calculus.…”

Section: Introductionmentioning

confidence: 98%

“…Then the aforementioned Hardy-Copson inequalities have been unified to an arbitrary time scale in the book 23 and in the papers [24][25][26][27][28][29][30][31] for the delta time scale calculus. In the delta time scale calculus, the reverse Hardy-Copson type inequalities, which are called delta Bennett-Leindler inequalities, can be found in previous works 28,[32][33][34] for 0 < q < 1. These results are unifications of discrete and continuous Bennett-Leindler inequalities mentioned above except the ones in Renaud.…”

Section: Introductionmentioning

confidence: 99%

“…By the following theorem, the discrete Bennett-Leindler inequality (9) and the continuous Bennett-Leindler inequality (13) are unified in Saker et al 34 for the delta time scale calculus.…”

Section: Introductionmentioning

confidence: 99%

“…By the following theorem, the discrete Bennett-Leindler inequality (10) and the continuous Bennett-Leindler inequality (14) are unified in Saker et al 34 for the delta time scale calculus. In this paper, the exponent of the constant L was computed as (1 − r)q which is not correct.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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“…By the following theorem, the reverse of the Bennett's (or Leindler's) inequality ( 7) is unified in Saker et al 34 for the delta time scale calculus.…”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

“…By the following theorem, the discrete Bennett-Leindler inequality (9) and the continuous Bennett-Leindler inequality (13) are unified in Saker et al 34 for the delta time scale calculus.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Diamond alpha Bennett‐Leindler type dynamic inequalities and their applications

Kayar

Kaymakçalan

Pelen

2021

Math Methods in App Sciences

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“…We can refer to the surveys [1,33] and the monograph [2] for exhibition of these results. The aforementioned Hardy-Copson inequalities have been unified to an arbitrary time scale in the book in [3] and in the articles in [4,[34][35][36][37][38][39][40] by using delta time scale calculus.…”

Section: Introductionmentioning

confidence: 99%

Hardy–Copson type inequalities for nabla time scale calculus

Kayar¹,

Kaymakçalan²

2021

Turk J Math

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This paper is devoted to the nabla unification of the discrete and continuous Hardy-Copson-type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.

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Novel Diamond Alpha Bennett–Leindler Type Dynamic Inequalities and Their Applications

Kayar

Kaymakçalan

2022

Bull. Malays. Math. Sci. Soc.

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Converses of Copson's inequalities on time scales

Cited by 10 publications

References 15 publications

Diamond alpha Bennett‐Leindler type dynamic inequalities and their applications

Diamond alpha Bennett‐Leindler type dynamic inequalities and their applications

Hardy–Copson type inequalities for nabla time scale calculus

Novel Diamond Alpha Bennett–Leindler Type Dynamic Inequalities and Their Applications

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