Hilbert-type inequalities for time scale nabla calculus

Abstract This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

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On a strengthened multidimensional Hilbert-type inequality

Mathematica Slovaca ◽

10.2478/s12175-014-0267-x ◽

2014 ◽

Vol 64 (5) ◽

Cited By ~ 1

Author(s):

Mario Krnić

Keyword(s):

Hölder’S Inequality ◽

Type Inequality ◽

Hölder's Inequality ◽

Weighted Functions ◽

Hilbert Type

AbstractThe main objective of this paper is a study of the general refinement and converse of the multidimensional Hilbert-type inequality in the so-called quotient form. Such extensions are deduced with the help of the sophisticated use of the well-known Hölder’s inequality. The obtained results are then applied to homogeneous kernels with the negative degree of homogeneity. Also, we establish the conditions under which the constant factors involved in the established inequalities are the best possible. Finally, we consider some particular settings with homogeneous kernels and weighted functions. In such a way we obtain both refinements and converses of some actual results, known from the literature.

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Consensus of classical and fractional inequalities having congruity on time scale calculus

General Mathematics ◽

10.2478/gm-2019-0006 ◽

2019 ◽

Vol 27 (1) ◽

pp. 57-69

Author(s):

Muhammad Jibril Shahab Sahir

Keyword(s):

Time Scales ◽

Time Scale ◽

Hölder’S Inequality ◽

Fractional Integrals ◽

Power Mean ◽

Extended Form ◽

Hölder's Inequality ◽

Time Scale Calculus ◽

Power Mean Inequality ◽

Radon’S Inequality

Abstract In this paper, we find accordance of some classical inequalities and fractional dynamic inequalities. We find inequalities such as Radon’s inequality, Bergström’s inequality, Rogers-Hölder’s inequality, Cauchy-Schwarz’s inequality, the weighted power mean inequality and Schlömilch’s inequality in generalized and extended form by using the Riemann-Liouville fractional integrals on time scales.

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More on Hölder’s Inequality and It’s Reverse via the Diamond-Alpha Integral

Symmetry ◽

10.3390/sym12101716 ◽

2020 ◽

Vol 12 (10) ◽

pp. 1716

Author(s):

M. Zakarya ◽

H. A. Abd El-Hamid ◽

Ghada AlNemer ◽

H. M. Rezk

Keyword(s):

Linear Combination ◽

Time Scales ◽

Time Scale ◽

Hölder’S Inequality ◽

Hölder's Inequality ◽

Special Cases ◽

General Time

In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when T=R.

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Some Dynamic Inequalities of Hilbert’s Type

Journal of Function Spaces ◽

10.1155/2020/4976050 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13 ◽

Cited By ~ 4

Author(s):

A. M. Ahmed ◽

Ghada AlNemer ◽

M. Zakarya ◽

H. M. Rezk

Keyword(s):

Time Scales ◽

Hölder’S Inequality ◽

Jensen’S Inequality ◽

Jensen's Inequality ◽

Hölder's Inequality ◽

Discrete Inequalities ◽

Special Case ◽

Hilbert Type

This paper is concerned with deriving some new dynamic Hilbert-type inequalities on time scales. The basic idea in proving the results is using some algebraic inequalities, Hölder’s inequality and Jensen’s inequality, on time scales. As a special case of our results, we will obtain some integrals and their corresponding discrete inequalities of Hilbert’s type.

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CONSONANCY OF DYNAMIC INEQUALITIES CORRELATED ON TIME SCALE CALCULUS

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.51.2020.3145 ◽

2020 ◽

Vol 51 (3) ◽

pp. 233-243

Author(s):

Muhammad Jibril Shahab Sahir

Keyword(s):

Time Scale ◽

Hölder’S Inequality ◽

Extended Form ◽

Hölder's Inequality ◽

Time Scale Calculus ◽

Radon’S Inequality

In this paper, discrete and continuous versions of some inequalitiessuch as Radon's Inequality, Bergstrom's Inequality, Nesbitt's Inequality,Rogers-Holder's Inequality and Schlomilch's Inequality are unified on dynamictime scale calculus in extended form.

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Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus

Communications in Mathematics ◽

10.2478/cm-2020-0023 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Muhammad Jibril Shahab Sahir

Keyword(s):

Time Scales ◽

Time Scale ◽

Hölder’S Inequality ◽

Hölder's Inequality ◽

Time Scale Calculus ◽

Radon’S Inequality

AbstractThe aim of this paper is to synthesize discrete and continuous versions of some dynamic inequalities such as Radon’s Inequality, Bergström’s Inequality, Schlömilch’s Inequality and Rogers-Hölder’s Inequality on time scales in comprehensive form.

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Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus

Mathematics ◽

10.3390/math8030434 ◽

2020 ◽

Vol 8 (3) ◽

pp. 434 ◽

Cited By ~ 2

Author(s):

Samir Saker ◽

Mohammed Kenawy ◽

Ghada AlNemer ◽

Mohammed Zakarya

Keyword(s):

Time Scales ◽

Time Scale ◽

Hölder’S Inequality ◽

Chain Rule ◽

Hölder's Inequality ◽

Conformable Calculus

In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When α = 1 we obtain some well-known time-scale inequalities due to Hardy, Copson, Bennett and Leindler inequalities.

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