Jessen's functional, its properties and applications

AbstractIn this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results, known from the literature. In particular, we obtain the whole series of refinements and converses of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young's inequality and Hölder's inequality

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Certain Properties of the Modified Degenerate Gamma Function

Journal of Mathematics ◽

10.1155/2021/8864131 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Kwara Nantomah

Keyword(s):

Gamma Function ◽

Hölder’S Inequality ◽

Mean Value ◽

Mean Value Theorem ◽

Young’S Inequality ◽

Hölder's Inequality ◽

Hadamard’S Inequality ◽

Parameter Variations ◽

Young's Inequality

In this paper, we prove some inequalities satisfied by the modified degenerate gamma function which was recently introduced. The tools employed include Holder’s inequality, mean value theorem, Hermite–Hadamard’s inequality, and Young’s inequality. By some parameter variations, the established results reduce to the corresponding results for the classical gamma function.

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On Some Inequalities for the Chaudhry-Zubair Extension of the Gamma Function

Asian Research Journal of Mathematics ◽

10.9734/arjom/2019/v14i130117 ◽

2019 ◽

pp. 1-9

Author(s):

Monica Atogpelge Atugba ◽

Kwara Nantomah

Keyword(s):

Gamma Function ◽

Hölder’S Inequality ◽

Minkowski’S Inequality ◽

Young’S Inequality ◽

Hölder's Inequality ◽

Analytical Tools ◽

Young's Inequality

By applying the classical Holder's inequality, Young's inequality, Minkowski's inequality and some other analytical tools, we establish some inequalities involving the Chaudhry-Zubair extension of the gamma function. The established results serve as generalizations of some known results in the literature.

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Jensen's Functionals on Time Scales

Journal of Function Spaces and Applications ◽

10.1155/2012/384045 ◽

2012 ◽

Vol 2012 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Matloob Anwar ◽

Rabia Bibi ◽

Martin Bohner ◽

Josip Pečarić

Keyword(s):

Time Scales ◽

Hölder’S Inequality ◽

Hölder's Inequality ◽

Power Means

We consider Jensen’s functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales. By applying the properties of Jensen’s functionals on these means, we obtain several refinements and converses of Hölder’s inequality on time scales.

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Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

Mathematics ◽

10.3390/math9233104 ◽

2021 ◽

Vol 9 (23) ◽

pp. 3104

Author(s):

Slavko Simić ◽

Vesna Todorčević

Keyword(s):

Generating Function ◽

Hölder’S Inequality ◽

Arithmetic Mean ◽

Hölder's Inequality ◽

Power Means ◽

Jensen Functional ◽

Exact Bounds ◽

Stolarsky Means

In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained.

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Extension of Hölder's inequality (I)

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700014192 ◽

1995 ◽

Vol 51 (3) ◽

pp. 369-375 ◽

Cited By ~ 6

Author(s):

E.G. Kwon

Keyword(s):

Geometric Mean ◽

Hölder’S Inequality ◽

Hölder's Inequality ◽

Continuous Form

A continuous form of Hölder's inequality is established and used to extend the inequality of Chuan on the arithmetic-geometric mean inequality.

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Hilbert-type inequalities for time scale nabla calculus

Advances in Difference Equations ◽

10.1186/s13662-020-03079-w ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

H. M. Rezk ◽

Ghada AlNemer ◽

H. A. Abd El-Hamid ◽

Abdel-Haleem Abdel-Aty ◽

Kottakkaran Sooppy Nisar ◽

...

Keyword(s):

Time Scale ◽

Hölder’S Inequality ◽

Hölder's Inequality ◽

Arbitrary Time ◽

Hilbert Type

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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