Minkowski and Beckenbach-Dresher inequalities and functionals on time scales

“…In a recent paper Bibi et al [3] established the Fubini's theorem on time scales while Barić et al [2] obtained a refined Jensen's inequality on time scales for superquadratic functions.These results are very useful in the proofs of our main results and for the reader's convenience, we recall these results before stating our main results in this section.…”

Section: Some Time Scale Inequalities For Superquadracitymentioning

confidence: 99%

Time scales Hardy-type inequalities via superquadracity

Oguntuase¹,

Persson²

2014

Ann. Funct. Anal.

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In this paper some new Hardy-type inequalities on time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardy-type inequalities involving superquadratic functions with general kernels to the case with arbitrary time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and discussed.

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“…In [2] Bibi et al, obtain integral forms of Minkowski's and Beckenbach-Dresher inequality on time scales.…”

Section: Introductionmentioning

confidence: 99%

Generalizations of Minkowski and Beckenbach–Dresher Inequalities and Functionals on Time Scales

Bibi

Rahman

Shahzad

2020

ijaa

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We generalize integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality.Using the Minkowski inequality (2.2) for integrals (Theorem 2.1), we have that this is nonnegative for p ≥ 1 and nonpositive for p < 1 and p = 0. Now we show (iii). If p ≥ 1 or p < 0, then using superadditivity andand the proof of (3.1) is established. If 0 < p < 1, then using subadditivity and negativity ofThe proof of (iv) is similar.Remark 3.2. Put X, Y ⊆ N, then for fixed F k and U l , the function M 2 has the form

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Minkowski and Beckenbach-Dresher inequalities and functionals on time scales

Cited by 48 publications

References 6 publications

Dynamic Hilbert-Type Inequalities with Fenchel-Legendre Transform

Dynamic Hilbert-Type Inequalities with Fenchel-Legendre Transform

Time scales Hardy-type inequalities via superquadracity

Generalizations of Minkowski and Beckenbach–Dresher Inequalities and Functionals on Time Scales

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