Some dynamic Hardy-type inequalities with general kernel

“…Remark 2.12 For r = 1, Corollary 2.7 and Example 2.2 provide refinements of Corollary 5.7 and Example 5.8 in [5], respectively. They also are a refinement of Theorem 1.1 in [29], but here we use time scales notation instead of the notation given in [29].…”

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confidence: 87%

“…In [5] (see also [22]) the authors proved that if (Ω, M, μ ) and (Λ, L, λ ) are two time scale measure spaces, k :…”

Section: Introductionmentioning

confidence: 99%

Refinement multidimensional dynamic inequalities with general kernels and measures

et al. 2019

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Using the properties of superquadratic and subquadratic functions, we establish some new refinement multidimensional dynamic inequalities of Hardy's type on time scales. Our results contain some of the recent results related to classical multidimensional Hardy's and Pólya-Knopp's inequalities on time scales. To show motivation of the paper, we apply our results to obtain some particular multidimensional cases and provide refinements of some Hardy-type inequalities known in the literature.

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“…Delta and nabla calculus were first two approaches in the theory of time scales. For introduction to the time scales calculus, the readers are referred to [9,10], and some related inequalities can be seen in [1,3,5,6,8,11,14].…”

Section: Introductionmentioning

confidence: 99%

Bivariate Montgomery identity for alpha diamond integrals

et al. 2019

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In the paper, some variants of Montgomery identity with the help of delta and nabla integrals are established which are useful to produce Montgomery identity involving alpha diamond integrals for function of two variables. The aforementioned identity is discussed in discrete, continuous, quantum calculus as well and employed to obtain Ostrowski type inequality for monotonically increasing function with respect to both parameters. MSC: Primary 26D15; secondary 39A13; 34N05- p(x, t) and q(y, s) are Peano kernels, defined in [12].

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Some dynamic Hardy-type inequalities with general kernel

Abstract: Abstract. In this paper, we extend some Hardy-type inequalities with certain kernels to arbitrary time scales. Certain classical and some new integral and discrete inequalities are deduced in seek of applications.Mathematics subject classification (2010): 26D15, 34N05, 28A25.

Cited by 21 publications

References 12 publications

Hardy-Type Inequalities on Time Scale via Convexity in Several Variables

Hardy-Type Inequalities on Time Scale via Convexity in Several Variables

Refinement multidimensional dynamic inequalities with general kernels and measures

Bivariate Montgomery identity for alpha diamond integrals

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