Some Integral Inequalities on Time Scales

Yin, Li; Qi, Feng

doi:10.1007/s00025-013-0320-z

Cited by 11 publications

(11 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As applications, next results present some refinements of some inequalities given by Qi and Yin, [12], in the cases of delta time-scale integral, the Cauchy nabla time-scales integrals and the Cauchy α-diamond time scale integrals.…”

Section: Proof By Lemma 3 and Hypothesis We Havementioning

confidence: 77%

“…In this section we give several variants of some inequalities from [12] in the case of isotonic linear functionals for p > 1 and 0 < r < 1 using the corresponding Holder's inequalities. ∈ L, f is positive and A(f ) ≥ A 2 (1) then…”

Section: Some Variants Of Qi's Inequality For Isotonic Linear Functiomentioning

confidence: 99%

“…Then we take the r-th power on both sides of the inequalities and have: A variant of Theorem 3.1 from [12] for isotonic linear functional can be the following: Theorem 6. Let E, L and A be such that L1, L2, A1, A2 are satisfied.…”

Section: Proof By Lemma 3 and Hypothesis We Havementioning

confidence: 99%

See 2 more Smart Citations

About some inequalities for isotonic linear functionals and applications

Ciurdariu¹

2014

ams

View full text Add to dashboard Cite

The aim of this paper is to establish some extensions of Holder's inequality, Minkowski's inequality and Qi's inequality for isotonic linear functionals taking into account that the time scale Cauchy delta, Cauchy nabla, α-diamond, multiple Riemann, and multiple Lebesque integrals all are isotonic linear functionals. Then several applications of these results for other particular isotonic linear functionals will be also obtaned. Mathematics Subject Classification: 26D15

show abstract

Section: Proof By Lemma 3 and Hypothesis We Havementioning

confidence: 77%

Section: Some Variants Of Qi's Inequality For Isotonic Linear Functiomentioning

confidence: 99%

See 1 more Smart Citation

About some inequalities for isotonic linear functionals and applications

Ciurdariu¹

2014

ams

View full text Add to dashboard Cite

show abstract

“…Using new generalizations of reverse of Young's inequality given in [7] and [8] will be given new inequalities for isotonic linear functionals starting from some results given in [10].…”

Section: Qi's Inequality For Isotonic Linear Functionalsmentioning

confidence: 99%

Holder-type and Qi-type inequalities for isotonic linear functionals

Ciurdariu¹

2016

ijma

View full text Add to dashboard Cite

show abstract

“…At first, one of the methods of the perturbation theory was referred to integral inequalities to quest some type of stability. In the last few years, the search was directed to the time scale integral inequalities by using diverse techniques and some significant results were obtained (see [8,30,24,25]). We are interested in further generalizing some nonlinear dynamic integral estimations.…”

Section: Introductionmentioning

confidence: 99%