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

Kayar, Zeynep; Kaymakçalan, Bıllûr

doi:10.1007/s40840-021-01224-6

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2022

2024

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Cited by 6 publications

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“…In particular, for a survey on classical inequalities on time scales, see [16], and for Riemann and Lebesgue integration on time scales, see [17]. Some other recent approaches in time scale calculus can be found in papers [18][19][20][21]. Further, for an overview of recent developments of multivariable time scale calculus, we refer the reader to [22].…”

Section: Definition 2 ([13]mentioning

confidence: 99%

New Diamond-α Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces

Kalamir

2022

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In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive σ-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales T and differential calculus on R, we obtain already-known Steffensen-type inequalities.

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